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Simple and Compound Interest, Stock

মোট প্রশ্ন৮৫৮এই পাতা১০০প্রতি পাতা১০০
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উত্তরিতবর্তমানপুনরায় দেখুনঅসম্পূর্ণ

Simple and Compound Interest, Stock

PrepBank · পাতা ১ / ৯ · ১–১০০ / ৮৫৮

১.
A bank offers 12% compound interest calculated half-yearly. A customer deposits Tk. 5000 on 1st January and another Tk. 5000 on 1st July of the same year. How much interest will he earn at the end of the year?
  1. ক
    Tk. 900
  2. খ
    Tk. 918
  3. গ
    Tk. 956
  4. ঘ
    Tk. 1020
ব্যাখ্যা

Question: A bank offers 12% compound interest calculated half-yearly. A customer deposits Tk. 5000 on 1st January and another Tk. 5000 on 1st July of the same year. How much interest will he earn at the end of the year?

Solution:
এখানে,
অর্ধ-বার্ষিক সুদের হার = 12% ÷ 2 = 6%
প্রথম জমা (1লা জানুয়ারী):
আসল, P1 = 5000 টাকা
সময়, n1 = 1 বছর = 2 অর্ধ-বছর
সুদের হার, r = 6%
চক্রবৃদ্ধি মূল (A1) = P1 (1 + r/100)n1
= 5000 × (1 + 6/100)2
= 5000 × (106/100)2
= 5000 × (106/100) × (106/100)
= 5618 টাকা

দ্বিতীয় জমা (1লা জুলাই):
আসল, P2 = 5000 টাকা
সময়, n2 = 6 মাস = 1 অর্ধ-বছর
সুদের হার, r = 6%
চক্রবৃদ্ধি মূল (A2) = P2 (1 + r/100)n2
= 5000 × (1 + 6/100)1
= 5000 × (106/100)
= 5300 টাকা

মোট প্রাপ্ত মূল = A1 + A2 = 5618 + 5300 = 10918 টাকা
মোট জমা = 5000 + 5000 = 10000 টাকা

∴ মোট অর্জিত সুদ = মোট প্রাপ্ত মূল - মোট জমা
= 10918 - 10000 = 918 টাকা

২.
A man deposits Tk. 5000 in a Bank at 10% interest rate compounded annually. At the end of the three year, the total amount including interest will become?
  1. ক
    ক) 605
  2. খ
    খ) 6655
  3. গ
    গ) 7755
  4. ঘ
    ঘ) 5566
ব্যাখ্যা
Question: A man deposits Tk. 5000 in a Bank at 10% interest rate compounded annually. At the end of the three year, the total amount including interest will become?

Solution: 
Given,
Principal, P = 5000 Tk.
Rate of interest, r = 10% = 10/100 = 1/10
Time, n = 3 years.

We know,
Compound Amount = P (1 + r)n
= 5000 × (1 + 1/10)3
= 5000 × (11/10)3
= 5000 × (11/10) × (11/10) × (11/10)
= 6655
৩.
If an investor gets Tk. 19,500 as interest after 5 years on his savings of Tk. 13,000. What is the rate of interest?
  1. ক
    ক) 8%
  2. খ
    খ) 5%
  3. গ
    গ) 10%
  4. ঘ
    ঘ) 30%
ব্যাখ্যা
Question: If an investor gets Tk. 19,500 as interest after 5 years on his savings of Tk. 13,000. What is the rate of interest?

Solution: 
এখানে
মুনাফা I = 19,500 টাকা 
আসল P = 13,000 টাকা 
সময় n = 5 বছর 
মুনাফার হার r  = ? 

আমরা জানি,
I = Pnr
r = I/Pn
  = {(19500 × 100)/(13000 × 5)}%
  = 30%
৪.
An amount of money is invested in a savings account for two years. It increased by Tk. 102.50 in two years after annual compounding at the rate of 5% per year. What is the amount invested initially?
  1. ক
    Tk. 800
  2. খ
    Tk. 1000
  3. গ
    Tk. 1250
  4. ঘ
    Tk. 1460
ব্যাখ্যা

Question: An amount of money is invested in a savings account for two years. It increased by Tk. 102.50 in two years after annual compounding at the rate of 5% per year. What is the amount invested initially?

Solution:
ধরি, আসল = P টাকা
সময়, n = 2 বছর
মুনাফার হার, r = 5% = 5/100 = 1/20
চক্রবৃদ্ধি মুনাফা = 102.50 টাকা

আমরা জানি, চক্রবৃদ্ধি মুনাফা = P(1 + r)n - P
⇒ P(1 + 1/20)2 - P = 102.50
⇒ P(21/20)2 - P = 102.50
⇒ P(441/400) - P = 102.50
⇒ (441P - 400P)/400 = 102.50
⇒ 41P/400 = 102.50
⇒ 41P = 102.50 × 400
⇒ 41P = 41000
⇒ P = 41000/41
∴ P = 1000

সুতরাং, শুরুতে বিনিয়োগকৃত আসলের পরিমাণ ছিল 1000 টাকা।

৫.
What is the difference between the compound interests on Tk. 5000 for 3/2 years at 4% per annum compounded yearly and half-yearly?
  1. ক
    ক) 5.78
  2. খ
    খ) 4.65
  3. গ
    গ) 3.24
  4. ঘ
    ঘ) 2.04
ব্যাখ্যা
C.I. when interest compound yearly
= Tk. [5000 × (1 + 4/100) (1 + 1/2 × 4/100)]
= Tk. 5304.

C.I. when interest is compounded half-yearly
= Tk. 5000 (1 + 2/100)3
= Tk. 5306.04

Difference
= Tk. (5306.04 - 5304)
= Tk. 2.04
৬.
A man invested Tk. 45000 when he bought Tk. 100 shares at Tk. 150. If 20% dividend is declared, find his annual income.
  1. ক
    Tk. 4500
  2. খ
    Tk. 3000
  3. গ
    Tk. 5000
  4. ঘ
    Tk. 6000
ব্যাখ্যা
Question: A man invested Tk. 45000 when he bought Tk. 100 shares at Tk. 150. If 20% dividend is declared, find his annual income.

Solution:
For Tk. 150 he get Tk. 20
∴ For Tk. 1 He get Tk. (20/150)
∴ For Tk. 45000 He get Tk. (20 × 45000)/150
= Tk. 6000
৭.
An amount of money is to be distributed among P, Q and R in the ratio of 2 : 7 : 9. The total of P’s and Q’s share is equal to R’s share. What is the difference between the shares of P and Q?
  1. ক
    5500
  2. খ
    8000
  3. গ
    9000
  4. ঘ
    Information inadequate
ব্যাখ্যা
Questions: An amount of money is to be distributed among P, Q and R in the ratio of 2 : 7 : 9. The total of P’s and Q’s share is equal to R’s share. What is the difference between the shares of P and Q?

Solution:
Let the amount to be distributed be Tk x.
P : Q : R = 2 : 7 : 9
Sum of the ratios = 2 + 7 + 9 = 18

P = (2/18) × x = x/9
Q = 7x/18
R = 9x/18 = x/2

As given, (x/9) + (7x/18) = (x/2)
⇒ (2x + 3x)/18 = (x/2)
⇒ x/2 = x/2
Thus, we get no conclusion. Amount should necessarily be known.
৮.
Find the annual income obtained by investing Tk 3000 in 5% debentures of face value Tk 100 at Tk 125?
  1. ক
    Tk 180
  2. খ
    Tk 120
  3. গ
    Tk 210
  4. ঘ
    None of the above
ব্যাখ্যা
Question: Find the annual income obtained by investing Tk 3000 in 5% debentures of face value Tk 100 at Tk 125?

Solution:
The number of debentures purchased = Tk. 3000/125
One debenture will give an income investment of Tk 100 × 5% = Tk 5.
So, total income = 5 × (3000/125) = Tk 120.
৯.
A bond gets matured in 10 years. Ram invested Tk. 42,000 in this bond and received Tk.1,05,000 once the bond matured. If the bond was under simple interest, then what was the rate of interest per annum?
  1. ক
    ক) 10%
  2. খ
    খ) 12.5%
  3. গ
    গ) 15%
  4. ঘ
    ঘ) 7.5%
ব্যাখ্যা
এখানে, 
সরল সুদের পরিমাণ =( ১,০৫,০০০ - ৪২,০০০) টাকা
                                = ৬৩,০০০ টাকা 
আমরা জানি 
সুদের পরিমাণ = আসল × হার×সময় / ১০০
       ৬৩০০০ = ৪২০০০ × হার × ১০ / ১০০
হার = ৬৩০০০× ১০০/৪২০০০× ১০ 
       = ১৫%
১০.
A certain sum of money becomes three times of itself in 20 years at simple interest. In how many years does it become double of itself at the same rate of simple interest?
  1. ক
    ক) 6 years
  2. খ
    খ) 9 years
  3. গ
    গ) 10 years
  4. ঘ
    ঘ) 8 years
ব্যাখ্যা
Let the principal be P.
After 20 years, Amount = 3P
SI = 3P - P = 2P

We know that, SI = PRT/100
                 ⇒ 2P = (P × R × 20)/100
                 ⇒ R = 10%

Now,
Amount = 2P
SI = Amount - Principal = 2P - P = P
⇒ SI = PRT/100
⇒ P = (P × 10 × T)/100
⇒ T = 10 years
১১.
4200 Taka is lent at compound interest of 10% per annum for 2 years. Find the amount after two years.
  1. ক
    Tk. 6068
  2. খ
    Tk. 5028
  3. গ
    Tk. 4082
  4. ঘ
    Tk. 5082
ব্যাখ্যা
Question: 4200 Taka is lent at compound interest of 10% per annum for 2 years. Find the amount after two years.

Solution:
Compound amount = P (1 + r)n
= 4200 {1 + (10/100)}2
= 4200 × (110/100) × (110/100)
= 42 × 11 × 11
= 5082
১২.
In a certain time, a sum becomes 4 times of itself on simple interest at the rate of 10% per annum. What is the rate of interest if the same sum becomes 7 times of itself in the same duration?
  1. ক
    20% 
  2. খ
    16% 
  3. গ
    21% 
  4. ঘ
    9% 
ব্যাখ্যা

Question: In a certain time, a sum becomes 4 times of itself on simple interest at the rate of 10% per annum. What is the rate of interest if the same sum becomes 7 times of itself in the same duration?

Solution:
Principal = P
Time = n (same in both cases)
Rate, r =  10%
Simple Interest, SI = 4P - P = 3P

We know,
SI = Prn 
⇒ 3P = (P × 10 × n)/100
⇒ 3P = (P × n)/10
∴ n = 30 years

Again,
In the second scenario, the same sum becomes 7 times itself in the same duration (30 years).
Final Amount, A = 7P
Simple Interest, SI = A - P = 7P - P = 6P
Time, n = 30 years

SI = Prn 
⇒ 6P = (P × r × 30)/100
⇒ 6 = (r × 3)/10
⇒ r = 60/3
∴ r = 20%

So the new rate of interest is 20% per annum.

১৩.
How many years will it take for an investment of Tk. 15000 to earn Tk. 3600 in simple interest rate of 4%?
  1. ক
    5 years
  2. খ
    6 years
  3. গ
    8 years
  4. ঘ
    4 years
ব্যাখ্যা

Question: How many years will it take for an investment of Tk. 15000 to earn Tk. 3600 in simple interest rate of 4%?

Solution:
Given that,
Principal, P = 15000
Simple Interest, I = 3600
Rate of interest, r = 4%
Time, n = ?

We know,
I = Pnr/100
⇒ n = (I × 100)/ (P × r)
= (3600 × 100)/(15000 × 4)
= 6

So, it will take 6 years for the investment to earn Tk. 3600 at 4% simple interest.

১৪.
Find the compound interest on Tk. 2000 at 15% interest per annum for 2 years, compounded annually-
  1. ক
    ক) Tk. 2245
  2. খ
    খ) Tk. 2345
  3. গ
    গ) Tk. 2545
  4. ঘ
    ঘ) Tk. 2645
ব্যাখ্যা
Question: Find the compound interest on Tk. 2000 at 15% interest per annum for 2 years, compounded annually-

Solution:
Compound Principal for 2 years = 2000(1 + 15/100)2
= 2000(115/100)2
= (2000 × 115 × 115)/(100 × 100)
= 2645 tk.
১৫.
A sum of money at compound interest doubles itself in 15 years. It will become eight times of itself in-
  1. ক
    40 years
  2. খ
    42 years
  3. গ
    45 years
  4. ঘ
    50 years
ব্যাখ্যা
Question:  A sum of money at compound interest doubles itself in 15 years. It will become eight times of itself in-

Solution: 
let the sum P 

2P = P (1 + r)15
⇒ (1 + r)15 = 2

let, sum will 8 times in n years
8P = P(1 + r)n
⇒ 8 = (1 + r)n
⇒ 23 = (1 + r)n
⇒ ((1 + r)15)3 = (1 + r)n
⇒ (1 + r)45 = (1 + r)n
∴ n = 45 years
১৬.
A person deposited Tk. 2500 for 4 years and Tk. 3600 for 3 years at the same rate of simple interest in a bank. If he received a total of Tk. 1040 as interest, what was the rate of interest per annum?
  1. ক
    5%
  2. খ
    8%
  3. গ
    11%
  4. ঘ
    15%
ব্যাখ্যা

Question: A person deposited Tk. 2500 for 4 years and Tk. 3600 for 3 years at the same rate of simple interest in a bank. If he received a total of Tk. 1040 as interest, what was the rate of interest per annum?

Solution:
ধরি, বার্ষিক সরল মুনাফার হার = r%

আমরা জানি, মুনাফা = (আসল × সময় × হার)/100

প্রথম ক্ষেত্রে মুনাফা = (2500 × 4 × r)/100 = 100r টাকা
দ্বিতীয় ক্ষেত্রে মুনাফা = (3600 × 3 × r)/100 = 108r টাকা

প্রশ্নমতে,
100r + 108r = 1040
⇒ 208r = 1040
⇒ r = 1040/208
⇒ r = 5

∴ বার্ষিক মুনাফার হার 5%

১৭.
A sum of money is put on C.I. for 2 years at 20%. It would fetch Tk. 482 more if the interest is payable half yearly than if it were payable yearly. Find the sum.
  1. ক
    Tk. 20000
  2. খ
    Tk. 15000
  3. গ
    Tk. 22000
  4. ঘ
    Tk. 28000
ব্যাখ্যা
Question: A sum of money is put on C.I. for 2 years at 20%. It would fetch Tk. 482 more if the interest is payable half yearly than if it were payable yearly. Find the sum.

Solution:
Let the Principal = Tk. 100
When compounded annually,
A = 100 [1+20/100]2 = 144

When compounded half yearly,
A = 100[1+10/100]4 = 146.41

Difference, 146.41 - 144 = 2.41
If difference is 2.41, then Principal = Tk. 100
If difference is 482, then Principal = (100 × 482)/2.41 = 20000
১৮.
4600 Taka is lent at compound interest of 10% per annum for 2 years. Find the amount after two years.
  1. ক
    Tk. 5656
  2. খ
    Tk. 5566
  3. গ
    Tk. 5556
  4. ঘ
    Tk. 6655
ব্যাখ্যা
Question: 4600 Taka is lent at compound interest of 10% per annum for 2 years. Find the amount after two years.

Solution:
Compound amount = P (1 + r)n
= 4600 {1 + (10/100)}2
= 4600 × (110/100) × (110/100)
= 46 × 11 × 11
= 5566
১৯.
A sum of money at simple interest amounts to Tk. 815 in 3 years and to Tk. 854 in 4 years. The sum is -
  1. ক
    ক) Tk.638
  2. খ
    খ) Tk.469
  3. গ
    গ) Tk.718
  4. ঘ
    ঘ) Tk. 698
ব্যাখ্যা
S. I for 1 year = Tk. (854 - 815)
                       = Tk. 39 
S. I for 3 years = Tk. (39 × 3) 
                        =  Tk. 117 

Principal = Tk. (815 - 117) = Tk. 698
২০.
Find the compound interest after 2 years on Tk. 14000 at the rate of interest 5% per annum.
  1. ক
    Tk. 15435
  2. খ
    Tk. 15400
  3. গ
    Tk. 1455
  4. ঘ
    Tk. 1400
  5. ঙ
    Tk. 1435
ব্যাখ্যা
Question: Find the compound interest after 2 years on Tk. 14000 at the rate of interest 5% per annum.

Solution:
Let the sum P = 14000.
Rate of interest = 5%
Period = 2 years

Hence, compound interest = 14000(1 + 5/100)2 - 14000
= 14000(1.05)2 - 14000
= 14000 × 1.05 × 1.05 - 14000
= 15435 - 14000
= 1435
২১.
A sum of money at simple interest amount to tk. 2,800 in 2 years and to tk. 3,250 in 5 years at a rate of:
  1. ক
    4%
  2. খ
    6%
  3. গ
    3%
  4. ঘ
    5%
ব্যাখ্যা
Question: A sum of money at simple interest amount to tk. 2,800 in 2 years and to tk. 3,250 in 5 years at a rate of:

Solution:
Simple interest for 3 years = (3250 - 2800) Tk.
= Tk. 450
∴ Simple Interest for 3 years =  Tk. 450
∴ Simple Interest for 5 years =  Tk. (450 × 5/3)
= Tk. 750

∴ Principal = 3250 - 750 = Tk. 2500

We know, 
I = Pnr
⇒ r = I/Pn
 ⇒ r = (750 × 100)/(2500 × 5)
∴ r = 6%
২২.
A moneylender charges Tk. 180 as simple interest on a sum of Tk. 600 for four months. What is the rate of interest per annum?
  1. ক
    80%
  2. খ
    85%
  3. গ
    90%
  4. ঘ
    95%
ব্যাখ্যা
Question: A moneylender charges Tk. 180 as simple interest on a sum of Tk. 600 for four months. What is the rate of interest per annum?

Solution:
Principal = Tk. 600
Interest = Tk. 180
Time = 4 months = 4/12 = 1/3 years
Rate of interest =R

Applying formula: Rate of Interest = (I × 100)/(P × t)
R = (180 × 100)/(600 × 1/3)
= (180 × 100)/200
= 90%
২৩.
Rana obtained an amount of Tk. 8376 as simple interest on a certain amount at 8 p.c.p.a. after 6 years. What is the amount invested by Rana?
  1. ক
    Tk. 18110
  2. খ
    Tk. 17180
  3. গ
    Tk. 17450
  4. ঘ
    Tk. 16450
ব্যাখ্যা
Question: Rana obtained an amount of Tk. 8376 as simple interest on a certain amount at 8 p.c.p.a. after 6 years. What is the amount invested by Rana?

Solution:
Simple interest, I = Tk. 8376
Rate of interest, r = 8%
Time, n = 6 years

We know,
I = Pnr
Or, P = I/nr
= (8376 × 100)/(6 × 8)
∴ P = 17450 Tk.
২৪.
A woman purchased 500 shares of the face value of Tk. 100 each from the market at Tk. 160 per share. If a dividend of 20% is declared, find her earning percent on the investment.
  1. ক
    10%
  2. খ
    12.5%
  3. গ
    15.1%
  4. ঘ
    16%
ব্যাখ্যা

Question: A woman purchased 500 shares of the face value of Tk. 100 each from the market at Tk. 160 per share. If a dividend of 20% is declared, find her earning percent on the investment.

Solution:
Given,
Price of 1 share (Market Value) = Tk. 160
∴ Price of 500 shares (Total Investment) = Tk. (160 × 500) = Tk. 80,000

Dividend per share = 20% of 100 = Tk. 20
∴ Total dividend income = 500 × 20 = Tk. 10,000

∴ Earning % = (Total Dividend/Total Investment) × 100
= (10,000/80,000) × 100
= (1/8) × 100
= 12.5%

২৫.
Tahsan took a loan at simple interest rate of 6 p.c.p.a. in the first year and it increased by 1.5 p.c.p.a. every year. If he pays Tk. 8190 as interest at the end of 3 years, what was his loan amount?
  1. ক
    Tk. 36500
  2. খ
    Tk. 36400
  3. গ
    Tk. 36800
  4. ঘ
    Tk. 35400
ব্যাখ্যা
Question: Tahsan took a loan at simple interest rate of 6 p.c.p.a. in the first year and it increased by 1.5 p.c.p.a. every year. If he pays Tk. 8190 as interest at the end of 3 years, what was his loan amount?

Solution:
Let the loan amount be Tk. x

ATQ,
6% of x  + 7.5% of x + 9% of x = 8190
⇒ (6x/100) + (7.5x/100) + (9x/100) = 8190
⇒ 22.5x = 819000
∴ x = 36400
২৬.
A sum of money amounts to Tk. 9800 after 5 years and Tk. 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is -
  1. ক
    15%
  2. খ
    5%
  3. গ
    12%
  4. ঘ
    8%
ব্যাখ্যা

Simple interest for 3 years
= 12005 - 9800
= 2205
Simple interest for 5 years
= (2205/3) × 5
= 3675
Some of money = 9800 - 3675
= 6125
R = (100 × 2205)/(6125 × 3)
= 12%

২৭.
In how many years Tk. 1000 will become Tk. 1331 at compound interest rate of 10% per annum?
  1. ক
    4 years
  2. খ
    6 years
  3. গ
    3 years
  4. ঘ
    9 years
ব্যাখ্যা

Question: In how many years Tk. 1000 will become Tk. 1331 at compound interest rate of 10% per annum?

Solution:
Given,
P = Tk. 1000
C = Tk. 1331
r = 10% p.a

We know,
P(1 + r)n = C
⇒ 1000(1 + 10%)n = 1331
⇒ (1 + 1/10)n = 1331/1000
⇒ (11/10)n = (11/10)3
∴ n = 3

∴ required time = 3 years

২৮.
Calculate the compound interest at the rate of 6% per annum for 2 years on the principal, which in 2 years at the rate of 2% per annum gives Tk. 8000 as simple interest.
  1. ক
    27420
  2. খ
    24720
  3. গ
    42770
  4. ঘ
    47270
ব্যাখ্যা
Question: Calculate the compound interest at the rate of 6% per annum for 2 years on the principal, which in 2 years at the rate of 2% per annum gives Tk. 8000 as simple interest.

Solution:
S.I. = PRT/100
⇒ P = (S.I. × 100) / (R × T)
∴ P = (8000 × 100)/(2 × 2) = 200000

A = 200000(1 + 6/100)2 = 200000(53/50)2 = 224720

C.I. = 224720 - 200000 = 24720.
২৯.
A sum of Tk. 800 amounts to Tk. 920 in 3 years at a certain simple interest rate. If the rate of interest is increased by 3% per annum, what will be the total amount after 3 years?
  1. ক
    Tk 668
  2. খ
    Tk 844 
  3. গ
    Tk 992
  4. ঘ
    Tk 998
  5. ঙ
    None
ব্যাখ্যা

Question: A sum of Tk. 800 amounts to Tk. 920 in 3 years at a certain simple interest rate. If the rate of interest is increased by 3% per annum, what will be the total amount after 3 years?

Solution:
Here, 
Sum = Tk 800, 
Amount = Tk 920,

∴ Simple interest = Amount - Principal 
= 920 - 800
= Tk 120

∴ Rate = (Interest × 100)/(Principal × Time)
= (120 × 100)/(800 × 3)
= 5% per annum

If the rate is increased by 3%, 
∴ Rate = 8% per annum

∴ simple interest = (800 × 8 × 3)/(800 × 3)
= Tk 192

∴ Amount = Principal + S.I.
= (800 + 192)
= Tk 992

৩০.
There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of Tk. 12,000 after 3 years at the same rate?
  1. ক
    3970
  2. খ
    3742
  3. গ
    3982
  4. ঘ
    3972
ব্যাখ্যা
Question: There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of Tk. 12,000 after 3 years at the same rate?

Solution: 
Let,P = Tk.100
Then, I = Tk. 60
and, T = 6years
we know,
I = Pnr/100
r = (I × 100)/Pn
= (60 × 100)/ (100 × 6)
= 10%

the compound principle of Tk. 12,000 after 3 years at the same rate wii be
C = P(1 + r)n
= 12000 ( 1 + 10/100)3
= 12000 ( 11/10)3
= 12000 (1331/1000)
= 12 × 1331
= 15972
∴ compound interest will be = (15972 - 12000)
= 3972 Tk.
৩১.
A sum of money at simple interest amounts to Tk. 815 in 3 years and to Tk. 854 in 4 years. The sum is-
  1. ক
    Tk. 689
  2. খ
    Tk. 869
  3. গ
    Tk. 968
  4. ঘ
    Tk. 698
ব্যাখ্যা
Question: A sum of money at simple interest amounts to Tk. 815 in 3 years and to Tk. 854 in 4 years. The sum is-

Solution:
Simple interest for 1 year = Tk. (854 - 815)
= Tk. 39

∴ Simple interest for 3 years = Tk.(39 × 3)
= Tk. 117

∴ Sum = (815 - 117)
= Tk. 698
৩২.
A sum of money amounts to Tk. 28000 in 2 years at 20% simple interest per annum. Find the sum.
  1. ক
    Tk. 20000
  2. খ
    Tk. 25000
  3. গ
    Tk. 22000
  4. ঘ
    Tk. 18000
  5. ঙ
    None of these
ব্যাখ্যা
Question: A sum of money amounts to Tk. 28000 in 2 years at 20% simple interest per annum. Find the sum.

Solution: 
Here,
A = 28000, T = 2, R = 20
⇒ A = P + SI
⇒ A = P + (P × R × T/100)
⇒ A = P [1 + (R × T/100)]
⇒ 28000 = P [1 + 0.4]
⇒ P = 28000/1.4
⇒ P = 20000
Thus, the required sum is Tk. 20000
৩৩.
A sum of money lent out at simple interest amounts Tk. 720 after 2 years and to Tk.1020 after a further period of 5 years. What is the sum ?
  1. ক
    ক) Tk. 450
  2. খ
    খ) Tk. 400
  3. গ
    গ) Tk. 480
  4. ঘ
    ঘ) Tk. 600
ব্যাখ্যা
⇒  S.I. for 2 years = Tk. 720.
⇒  S.I. for 7 years = Tk. 1020
∴   S.I. for 5 years = Tk. 1020 - Tk. 720= Tk. 300.

S.I. for 2 years =(300​/5) × 2= Tk..120
Principal=720 - 120 = Tk. 600
∴  The sum is Tk. 600.
৩৪.
A sum of money becomes 7/6 of itself in 3 years at a certain rate of simple interest. What is the rate of interest per annum?
  1. ক
    (50/9)%
  2. খ
    (60/9)%
  3. গ
    (70/9)%
  4. ঘ
    (55/9)%
  5. ঙ
    (51/9)%
ব্যাখ্যা
Let principal = 6y
Hence, Amount = 6y × 7/6 = 7y
simple interest = 7y - 6y = y
If time 3 years, then simple interest,
y = 6yr × 3/100 [r = rate of simple interest]
or, r = 50/9
৩৫.
In how many years, Tk. 150 will produce the same interest @ 8% as Tk. 800 produce in 3 years @ (9/2)% ?
  1. ক
    6
  2. খ
    8
  3. গ
    9
  4. ঘ
    12
ব্যাখ্যা
Question: In how many years, Tk.150 will produce the same interest at 8% as Tk.800 produce in 3 years at 9/2%

Solution:
Here 
P =Tk.800,
r = 9/2​%.
n = 3 years
∴S.I.=Tk.(800 × 9 × 3)/(2 × 100)​ = Tk.108

Now,
S.I.= Tk.108
P = Tk.150,
r = 8% =8/100

We know
I = Pnr
n = I/Pr
   = 108/(150 × 8/100) 
   = (100 × 108)/(150 × 8)
   = 9 years
৩৬.
What yearly income can be earned by investing Tk. 14400 in 15% stock at Tk. 120?
  1. ক
    Tk. 1600
  2. খ
    Tk. 1750
  3. গ
    Tk. 1850
  4. ঘ
    Tk. 1800
ব্যাখ্যা
Question: What yearly income can be earned by investing Tk. 14400 in 15% stock at Tk. 120?

Solution:
15% stock at Tk. 120 বলতে বুঝায় স্টকটির ফেস ভ্যালু ১০০ টাকায় ১৫ টাকা লাভ হয় এবং স্টকটির বাজার মূল্য ১২০ টাকা।

এখানে,
১২০ টাকা বিনিয়োগ করে আয় হয় ১৫ টাকা 
∴ ১ টাকা বিনিয়োগ করে আয় হয় ১৫/১২০ টাকা 
∴ ১৪৪০০ টাকা বিনিয়োগ করে আয় হয় (১৪৪০০ × ১৫)/১২০ টাকা
= ১৮০০ টাকা 
৩৭.
A borrows sum of TK. 90000 for 4 years at 5% simple interest. He lends it to B at 7% for 4 years at simple interest. What is his gain?
  1. ক
    8690
  2. খ
    7200
  3. গ
    5820
  4. ঘ
    6470
  5. ঙ
    7890
ব্যাখ্যা

Question: A borrows sum of TK. 90000 for 4 years at 5% simple interest. He lends it to B at 7% for 4 years at simple interest. What is his gain?

Solution:
A's, Principal = TK. 90000
simple interest rate = 5%
time = 4 years

∴ simple interest = TK. (90000 × 4 × 5)/100
= TK. 18000

B's, Principal = TK. 90000
simple interest rate = 7%
time = 4 years

∴ simple interest = TK. (90000 × 4 × 7)/100
= TK. 25200

∴ Profit of A = TK. (25200 - 18000) = TK. 7200

৩৮.
A sum of money at compound interest doubles itself in 15 years. It will become eight times of itself in-
  1. ক
    ক) 15 years
  2. খ
    খ) 30 years
  3. গ
    গ) 45 years
  4. ঘ
    ঘ) 60 years
ব্যাখ্যা
Question: A sum of money at compound interest doubles itself in 15 years. It will become eight times of itself in-

Solution: 
let the sum P 

2P = P (1 + r)15
⇒ (1 + r)15 = 2

let, sum will 4 times in n years
8P = P(1 + r)n
⇒ 8 = (1 + r)n
⇒ 23 = (1 + r)n
⇒ ((1 + r)15)3 = (1 + r)n
⇒ (1 + r)45 = (1 + r)n
∴ n = 45 years
৩৯.
If an investor gets Tk. 17,500 as interest after 5 years on his savings of Tk. 14,000. What is the rate of interest?
  1. ক
    ক) 12%
  2. খ
    খ) 20%
  3. গ
    গ) 25%
  4. ঘ
    ঘ) 30%
ব্যাখ্যা
Question: If an investor gets Tk. 17,500 as interest after 5 years on his savings of Tk. 14,000. What is the rate of interest?

Solution: 
এখানে
মুনাফা I = 17,500 টাকা 
আসল P = 14,000টাকা 
সময় n = 5 বছর 
মুনাফার হার r  = ? 

আমরা জানি,
I = Pnr
r = I/Pn
  = {(17,500 × 100)/(14,000 × 5)}%
  = 25%
৪০.
In how many years will Tk. 750 amount to Tk. 900 at 4% simple interest per annum?
  1. ক
    3.5 years
  2. খ
    3 years
  3. গ
    4.5 years
  4. ঘ
    5 years
ব্যাখ্যা

Question: In how many years will Tk. 750 amount to Tk. 900 at 4% simple interest per annum?

Solution:
Simple Interest = Amount - Principal
= 900 - 750
= 150

Here,
Principal, P = 750
Interest Rate, R = 4%
SI = 150
Time, T = ?

SI = PRT/100
⇒  T = (SI × 100)/(P × R)
= (150 × 100)/(750 × 4)
= 15000/3000
= 5 years

৪১.
The simple interest at p% for p years will be Tk. p on a sum of?
  1. ক
    Tk. p
  2. খ
    Tk. 100p
  3. গ
    Tk. p/100
  4. ঘ
    Tk. 100/p
ব্যাখ্যা

Question: The simple interest at p% for p years will be Tk. p on a sum of?

Given,
Rate of interest, r = p%
Interest, I = p Tk.
Time, n = p years.

We know,
I = Pnr
P = I/nr
= (p × 100)/(p × p)
= 100/p Tk.

৪২.
কোনো শহরের বর্তমান জনসংখ্যা ৪ লক্ষ। শহরটির জনসংখ্যা বৃদ্ধির হার শতকরা ২৫ জন হলে, ২ বছর পরে শহরের জনসংখ্যা কত হবে?
  1. ক
    ক) ৬,২৫,০০০
  2. খ
    খ) ৬,৫০,০০০
  3. গ
    গ) ৫,৫০,০০০
  4. ঘ
    ঘ) ৫,২৫,০০০
ব্যাখ্যা
প্রশ্ন: কোনো শহরের বর্তমান জনসংখ্যা ৪ লক্ষ। শহরটির জনসংখ্যা বৃদ্ধির হার শতকরা ২৫ জন হলে, ২ বছর পরে শহরের জনসংখ্যা কত হবে?

সমাধান:
আমরা জানি,
জনসংখ্যা বৃদ্ধির হার চক্রবৃদ্ধি হারে গণনা করা হয়। 

দেওয়া আছে,
জনসংখ্যা বৃদ্ধির হার, r = ২৫/১০০ = ০.২৫ 
জনসংখ্যা, P = ৪০০০০০ জন 
সময়, n = ২ বছর 

২ বছর পরে শহরের জনসংখ্যা হবে
C = P( ১ + r)n জন 
= ৪০০০০০(১ + ০.২৫)২ জন 
= ৪০০০০০ × ১.২৫ × ১.২৫ জন 
= ৬২৫০০০ জন  
৪৩.
What would be the compound interest accrued on an amount of Tk 10000 at the rate of 15% per annum in 2 years? 
  1. ক
    ক) 2100 Tk
  2. খ
    খ) 3225 Tk
  3. গ
    গ) 1800 Tk
  4. ঘ
    ঘ) 2420 Tk
ব্যাখ্যা
Question: What would be the compound interest accrued on an amount of Tk 10000 at the rate of 15% per annum in 2 years? 

Solution:
Compound Principal = 10000(1 + 15/100)2
= 10000 × (115/100)2
= (10000 × 115 × 115)/(100 × 100)
= 13225

Compound interest = 13225 - 10000 = 3225
৪৪.
A man purchased 300 shares of the face value of Tk. 100 each from the market at Tk. 800 per share. If a dividend of 24% is declared, find his earning percent on the investment.
  1. ক
    2.4%
  2. খ
    30%
  3. গ
    8%
  4. ঘ
    3%
ব্যাখ্যা
Question: A man purchased 300 shares of the face value of Tk. 100 each from the market at Tk. 800 per share. If a dividend of 24% is declared, find his earning percent on the investment.

Solution:
১টি শেয়ারের বাজারমূল্য ৮০০ টাকা 
শেয়ারটির ফেস ভ্যালু বা অভিহিত মূল্য ১০০ টাকা 

শেয়ারের লাভ বা ক্ষতি সবসময় শেয়ারের ফেসভ্যালু বা অভিহিত মূল্যের উপর হয়। বাজারমূল্যের উপর নয়। অর্থাৎ, এখানে যে ২৪% লাভের কথা বলা আছে তা মূলত ১০০ টাকার লভ্যাংশ, ৮০০ টাকার নয়।
মোট কথা মানুষটি প্রতিটি শেয়ারের জন্য ৮০০ টাকা খরচ করে লাভ করবে ২৪ টাকা, (২৪ × ৮) = ১৯২ টাকা নয়।

তাহলে,
৮০০ টাকা বিনিয়োগ করে লাভ করেন ২৪ টাকা 
∴ ১ টাকা বিনিয়োগ করে লাভ করেন ২৪/৮০০ টাকা 
∴ ১০০ টাকা বিনিয়োগ করে লাভ করেন (২৪ × ১০০)/৮০০ টাকা 
= ৩ টাকা  

∴ সে তাঁর বিনিয়োগের ৩% লাভ করবে।
৪৫.
A sum of money doubles itself in 5 years at a certain rate of simple interest. In how many years will it become five times itself at the same rate of interest?
  1. ক
    20 years
  2. খ
    25 years
  3. গ
    18 years
  4. ঘ
    15 years
ব্যাখ্যা

Question: A sum of money doubles itself in 5 years at a certain rate of simple interest. In how many years will it become five times itself at the same rate of interest?

Solution:
Let the Principal be P.
The amount doubles in 5 years, so Amount = 2P.
Interest (I) for 5 years = 2P - P = P.

Now, the sum needs to become five times itself, so New Amount = 5P.
Required Interest (I) = 5P - P = 4P.

We know that,
P amount of interest is earned in = 5 years.
∴ 4P amount of interest will be earned in = (5 × 4) years = 20 years.

∴ The sum of money will become five times itself in 20 years.

৪৬.
Hasan lent Tk. 400 to Asif for 2 years and Tk. 100 to Ratul for 4 years and received together from both Tk. 60 as interest. What is the rate of interest if the simple interest rate of both is the same?
  1. ক
    4%
  2. খ
    3%
  3. গ
    5%
  4. ঘ
    6%
ব্যাখ্যা
Question: Hasan lent Tk. 400 to Asif for 2 years and Tk. 100 to Ratul for 4 years and received together from both Tk. 60 as interest. What is the rate of interest if the simple interest rate of both is the same?

Solution:
Let
rate is r%
The interest of Asif, I1 = 400 × 2 × r%
The interest of Ratul, I2 = 100 × 4 × r%

According to the question,
{(400 × 2 × r)/100} + {(100 × 4 × r)/100} = 60
Or, 8r + 4r = 60
Or, 12r = 60
Or, r = 60/12
∴ r = 5%
৪৭.
What is the difference between simple and compound interest at 5% per annum on a sum of Tk. 8000 at the end of 2 years?
  1. ক
    Tk. 20
  2. খ
    Tk. 32
  3. গ
    Tk. 50
  4. ঘ
    Tk. 64
ব্যাখ্যা

Question: What is the difference between simple and compound interest at 5% per annum on a sum of Tk. 8000 at the end of 2 years?

Solution:
এখানে,
মূলধন (P) = 8000 টাকা
সুদের হার (r) = 5%
সময় (n) = 2 বছর

সরল সুদ (SI):
SI = (P × r × n)/100
= (8000 × 5 × 2)/100
= 800 টাকা

চক্রবৃদ্ধি সুদ (CI):
A = P(1 + r/100)n
= 8000(1 + 5/100)2
= 8000(105/100)2
= 8000 × (105/100) × (105/100)
= 8820 টাকা

চক্রবৃদ্ধি সুদ (CI) = A - P
= 8820 - 8000
= 820 টাকা

∴ সুদের পার্থক্য = CI - SI
= 820 - 800
= 20 টাকা

৪৮.
A sum of money doubles itself in 10 years. How many years will it take to triple itself?
  1. ক
    ক) 20
  2. খ
    খ) 30
  3. গ
    গ) 25
  4. ঘ
    ঘ) 40
  5. ঙ
    ঙ) 35
ব্যাখ্যা

Let P = 100,
A = 200,
It means I = 100

Now We want A = 300,
means I = 200
Years for I of Tk. 100 = 10
Years for I of Tk. 200 = (10/100) × 200 = 20 Years

Alternative Method:
Assuming simple interest, let the amount be P and rate of interest per annum be R%.

Given that P becomes 2P in 10 years.
=> P + PX10X R/100 = 2P
=> 1 + R/10 = 2
=> R = 10

Let P triple itself in N years:
=> P + PXNX 10/100 = 3P
=> 1 + N/10 = 3
=> N = 20 years

৪৯.
At a certain time, the ratio of a certain principal and interest obtained from it are in the ratio 10 : 3 at 10% interest per annum. The number of years for which the money was invested is =?
  1. ক
    7 years
  2. খ
    4 years
  3. গ
    5 years
  4. ঘ
    3 years
  5. ঙ
    None of the above
ব্যাখ্যা
Question: At a certain time, the ratio of a certain principal and interest obtained from it are in the ratio 10 : 3 at 10% interest per annum. The number of years for which the money was invested is =?

Solution:
According to the question,
Principal = 10
Interest = 3

We know, T = (100 × S.I.)/(P × R)
= (100 × 3)/(10 × 10)
= 300/100
= 3 years
৫০.
Tk.5000 is deposited in a savings account which pays 7% annual interest compounded semi - annually. To the nearest tk how much is at the end of the year?
  1. ক
    ক) 5423
  2. খ
    খ) 5356
  3. গ
    গ) 5122
  4. ঘ
    ঘ) 5247
ব্যাখ্যা

১ম 6 মাসে মুনাফা = 5000 × 6/12 × 7/100 = 175
২য় 6 মাসে মুনাফা = 5175 × 6/12 × 7/100 = 362.25/2 = 181.125
∴ বছর শেষে মোট টাকার পরিমান = 5000 + 175 + 181.125 = 5356.125 ≈ 5356

৫১.
What is the total interest on Tk 2,000 at 12.5% per annum for 9 months (in taka)?
  1. ক
    Tk. 150
  2. খ
    Tk. 210.5
  3. গ
    Tk. 187.5
  4. ঘ
    Tk. 190
ব্যাখ্যা

Question: What is the total interest on Tk 2,000 at 12.5% per annum for 9 months (in taka)?

সমাধান:
আসল, P = 2,000 টাকা
সুদের হার, r = 12.5% = 12.5/100 = 1/8
সময়, n = 9 মাস = 9/12 = 3/4 বছর

সুদ, I = Pnr
⇒ সুদ, I = 2,000 × (3/4) × (1/8)
∴ সুদ, I = 187.5 টাকা

৫২.
A sum of TK. 800 amounts to TK. 920 in 3 years at simple interest. What will it amount to if the rate of interest is increased by 3%?
  1. ক
    Tk. 1012
  2. খ
    TK. 972
  3. গ
    Tk. 980
  4. ঘ
    Tk. 992
ব্যাখ্যা

Question: A sum of TK. 800 amounts to TK. 920 in 3 years at simple interest. What will it amount to if the rate of interest is increased by 3%?

Solution:
Principal (P) = 800 TK.
Amount after 3 years = 920 TK.
∴ Simple Interest (SI) for 3 years = 920 - 800 = 120 TK.

Now, SI = (P × n × r)/100
⇒ 120 = (800 × 3 × r)/100
⇒ 120 = 24r
⇒ r = 120/24
∴ r = 5%

New Interest Rate = 5% + 3% = 8%
New simple interest for 3 years = (800 × 3 × 8) / 100 = 192 TK.
New Amount = Principal + New Interest = 800 + 192 = 992 TK.

Alternative Shortcut Method:
Additional Interest for 3% increase in 3 years = (800 × 3 × 3)/100 = 72 TK.
∴ New Amount = 920 + 72 = 992 TK.

৫৩.
A sum of money amounts to 13675 taka after 5 years and 15880 taka after 8 years at the same rate of simple interest. What is the rate of interest per annum?
  1. ক
    7%
  2. খ
    8%
  3. গ
    7.85%
  4. ঘ
    7.35%
  5. ঙ
    12%
ব্যাখ্যা
Simple interest for 3 years = (15880 −13675) taka
                                            = 2205 taka
Simple interest for 5 years = 2205 × 5/3 taka
                                            = 3675 taka
Principle = (13675 - 3675) taka
                = 10000 taka
Therefore, rate = 100 × 3675/(10000 × 5) %
                         = 7.35%
৫৪.
A certain sum will amount to Tk. 12100 in 2 years at 10% per annum of compound interest, interest being compounded annually. The sum is = ?
  1. ক
    Tk. 12000
  2. খ
    Tk. 6000
  3. গ
    Tk. 8000
  4. ঘ
    Tk. 10000
ব্যাখ্যা
Question: A certain sum will amount to Tk. 12100 in 2 years at 10% per annum of compound interest, interest being compounded annually. The sum is = ?

Solution:
Given,
Amount = 12,100; r = 10%, t = 2 yrs
৫৫.
The cost price of a Tk 100 stock at 4 discount, when brokerage is 1/4% is:
  1. ক
    ক) 95.75
  2. খ
    খ) 96
  3. গ
    গ) 96.25
  4. ঘ
    ঘ) 104.25
ব্যাখ্যা
C.P. = (100 - 4 + 1/4 ) = tk 96.25
৫৬.
A person takes a loan of Tk. 200 at 5% simple interest. He returns Tk.100 at the end of one year. In order clear his dues at the end of 2 year, he would pay :
  1. ক
    ক) Tk. 100
  2. খ
    খ) Tk. 105
  3. গ
    গ) Tk. 115
  4. ঘ
    ঘ) Tk. 110
ব্যাখ্যা
Amount to be paid = Tk.[100+(200×5×1)/100+(100×5×1)/100] = Tk. 115.
৫৭.
The simple interest on a certain sum of money for 5 years at 10% per annum is Tk. 150 less than the simple interest on the same sum for 7 years at  8% per annum. Find the sum.
  1. ক
    Tk. 7500
  2. খ
    Tk. 3500
  3. গ
    Tk. 2500
  4. ঘ
    Tk. 1500
ব্যাখ্যা
Question: The simple interest on a certain sum of money for 5 years at 10% per annum is Tk. 150 less than the simple interest on the same sum for 7 years at  8% per annum. Find the sum.

Solution: 
Let,
sum = x taka 

ATQ, 
{x × (8/100) × 7} - {x × (10/100) × 5} = 150 
⇒ (14x/25) - (x/2) = 150 
⇒ (28x - 25x)/50 = 150 
⇒ 3x/50 = 150 
⇒ x/50 = 50 
∴ x = 2500
৫৮.
The banker's gain on a bill due 1 year hence at 12% per annum is Tk. 6. The true discount is:
  1. ক
    ক) 72
  2. খ
    খ) 36
  3. গ
    গ) 54
  4. ঘ
    ঘ) 50
ব্যাখ্যা

T.D. = (B.G.×100)/(R×T)
= Tk.(6×100 / 12×1)
= Tk.50

৫৯.
The simple interest on a sum of money in 5 years at 12% per annum is Tk. 500 less than the simple interest accrued on the same sum in 7 years at 10% per annum. Find the sum.
  1. ক
    Tk. 4000
  2. খ
    Tk. 4500
  3. গ
    Tk. 5000
  4. ঘ
    Tk. 5500
ব্যাখ্যা
Question: The simple interest on a sum of money in 5 years at 12% per annum is Tk. 500 less than the simple interest accrued on the same sum in 7 years at 10% per annum. Find the sum.

Solution: 
Let the sum be P.
SI in 5 years at 12% per annum = P × 12 × (5/100) = 0.6 P
SI in 7 years at 10% per annum = P × 10 × (7/100) = 0.7 P

Now, according to the question,
0.7 P - 0.6 P = 500
⇒ 0.1 P = 500
⇒ P = 5000
Thus, the required sum is Tk. 5000
৬০.
The simple interest on a certain sum of money at the rate of 5 p.a. for 8 years is Tk. 840. The rate of interest for which the same amount of interest can be received on the same sum after 5 years is:
  1. ক
    ক) 6%
  2. খ
    খ) 8%
  3. গ
    গ) 9%
  4. ঘ
    ঘ) 10%
ব্যাখ্যা
S.I =Tk. 840
R = 5%
T = 8 years
Principal = (100 × 840)/(5 × 8)
              = Tk. 2100

Again 
S.I =Tk. 840
Principal = Tk. 2100
T = 5 years
Rate = (100 × 840)/(2100 × 5)
        = 8%
৬১.
If the simple interest on Tk. N at N% per annum for 5 years amounts to Tk. 2N, what is the value of N?
  1. ক
    40
  2. খ
    20
  3. গ
    30
  4. ঘ
    44
  5. ঙ
    None
ব্যাখ্যা

Question: If the simple interest on Tk. N at N% per annum for 5 years amounts to Tk. 2N, what is the value of N?

Solution:
Given,
Principal, P = N
Rate, r = N% = N/100
Time, n = 5 years
Simple Interest, I = 2N

We know,
I = (P × r × n)/100
⇒ 2N = N × (N/100) × 5
⇒ 2N = 5N2/100
⇒ 2N × 100 = 5N2
⇒ 200N = 5N2
⇒ N2 = 40N
⇒ N = 40

∴ The value of N = 40

৬২.
Find the difference between the simple interest and the compound interest at 5% per annum for 2 years on a principal of Tk 4000.
  1. ক
    5 Tk
  2. খ
    10 Tk
  3. গ
    15 Tk
  4. ঘ
    20 Tk
ব্যাখ্যা
Question: Find the difference between the simple interest and the compound interest at 5% per annum for 2 years on a principal of Tk 4000.

Solution:
We know, Simple Interest, I = Pnr
and Compound Principal, C = p(1 + r)n

Simple Interest = 4000 × 2 × (5/100) = 400 Tk

Compound Principal = 4000 × {1 + (5/100)}2
= 4000 × (105/100)2
= (4000 × 105 × 105)/(100× 100)
= 4410

So, Compound interest = 4410 - 4000 = 410 Tk
So, difference = 410 - 400 = 10 Tk
৬৩.
Find the difference between the simple and the compound interest on a principal of Tk 2000 for 2 years at 15% per annum.
  1. ক
    35 Tk
  2. খ
    45 Tk
  3. গ
    50 Tk
  4. ঘ
    60 Tk
  5. ঙ
    72 Tk
ব্যাখ্যা
Question: Find the difference between the simple and the compound interest on a principal of Tk 2000 for 2 years at 15% per annum.

Solution:
আসল,P =2000
সময়, n = 2বছর
মুনাফার হার, r =15% =15/100 =0.15

∴ সরল মুনাফা = Prn
= 2000 × (15/100) × 2
= 600

∴ চক্রবৃদ্ধি মুনাফার = P(1 + r)n - P
= 2000(1 + 0.15)2 - 2000
= 2645 -2000
= 645

∴ পার্থক্য = 645 - 600
= 45
৬৪.
A sum of money amounts to Tk 9800 after 5 years and Tk. 12005. after 8 years at the same rate of simple interest. The rate of interest per annum is -
  1. ক
    15%
  2. খ
    12%
  3. গ
    8%
  4. ঘ
    5%
ব্যাখ্যা
Question: A sum of money amounts to Tk 9800 after 5 years and Tk. 12005. after 8 years at the same rate of simple interest. The rate of interest per annum is -

Solution: 
Simple interest for 3 years
= 12005 - 9800 = 2205
Simple interest for 5 years
= (2205/3) × 5 = 3675

Some of money = 9800 - 3675 = 6125

∴ Rate of interest = (100 × 2205)/(6125 × 3)
= 12%
৬৫.
At simple interest of 5%, 6% and 8% for three consecutive years, the interest earned is Tk. 760. Find The principle? 
  1. ক
    ক) Tk. 4,000
  2. খ
    খ) Tk. 4,600
  3. গ
    গ) Tk. 3,200
  4. ঘ
    ঘ) Tk. 3,600
ব্যাখ্যা
ধরি, 
আসল x টাকা 

প্রশ্নমতে,
{( x×1×5) +(x×1×6 )+(x×1×8)} /100 = 760 
(5x +6x +8x) /100 = 760
19x/100 = 760  
x = (760 × 100)/19 
  = 4000
৬৬.
An amount of Tk 10000 becomes Tk 11025 in 1 year if the interest is compounded half-yearly. What is the rate of compound interest per annum?
  1. ক
    7%
  2. খ
    8%
  3. গ
    9%
  4. ঘ
    10%
ব্যাখ্যা
Question: An amount of Tk 10000 becomes Tk 11025 in 1 year if the interest is compounded half-yearly. What is the rate of compound interest per annum?

Solution:
Let the compound interest be r

ATQ,
10000 × {1 + (r/2)}2 = 11025
⇒ {(2 + r)/2}2 = 11025/10000
⇒ (2 + r)/2 = 105/100 [applying square root]
⇒ 2 + r  = 210/100
⇒ 200 + 100r = 210
⇒ 100r = 10
⇒ r = 10/100
⇒ r = (10/100) × 100%
⇒ r  = 10%
৬৭.
How many shares of market value Tk. 25 each can be purchased for Tk.15300, brokerage being 2% ? 
  1. ক
    ক) 450
  2. খ
    খ) 400
  3. গ
    গ) 550
  4. ঘ
    ঘ) 600
ব্যাখ্যা
CP of each share = Tk. (25 + 2% of 25) = Tk. 25.50. 

Number of shares= 15300/25.50
                             = 600
৬৮.
What would be the compound interest accrued on an amount of Tk 10000 at the rate of 15% per annum in 2 years? 
  1. ক
    Tk. 2325
  2. খ
    Tk. 1825
  3. গ
    Tk. 3225
  4. ঘ
    Tk. 4225
ব্যাখ্যা
Question: What would be the compound interest accrued on an amount of Tk 10000 at the rate of 15% per annum in 2 years? 

Solution:
Compound Principal = 10000(1 + 15/100)2
= 10000 × (115/100)2
= (10000 × 115 × 115)/(100 × 100)
= 13225

∴ Compound interest = 13225 - 10000 = 3225
৬৯.
How many years will it take for an investment of Tk. 10000 to earn Tk. 3000 in simple interest at a rate of 6%?
  1. ক
    3 years
  2. খ
    4 years
  3. গ
    5 years
  4. ঘ
    6 years
ব্যাখ্যা

Question: How many years will it take for an investment of Tk. 10000 to earn Tk. 3000 in simple interest at a rate of 6%?

Solution:
Given that,
Principal, P = 10000
Simple Interest, I = 3000
Rate of interest, r = 6%
Time, n = ?

We know,
I = Pnr/100
⇒ 3000 = (10000 × n × 6)/100
⇒ 3000 = 100 × n × 6
⇒ 3000 = 600n
⇒ n = 3000/600
⇒ n = 5

So, it will take 5 years for the investment to earn Tk. 3000 at 6% simple interest.

৭০.
On a certain sum of money, the simple interest for 2 years is Tk. 350 at the rate of 4% per annum. If it was invested at compound interest at the same rate for the same duration as before, how much more interest would be earned?
  1. ক
    Tk. 3.75
  2. খ
    Tk. 7
  3. গ
    Tk. 9
  4. ঘ
    Tk.35
ব্যাখ্যা
Question: On a certain sum of money, the simple interest for 2 years is Tk. 350 at the rate of 4% per annum. If it was invested at compound interest at the same rate for the same duration as before, how much more interest would be earned?

Solution: 
let, the sum be P 

350 = P × 2 × 4/100 
⇒ 350 = P × 2/25
⇒ P = 4375 

compounded interest = 4375 (1 + .04)2 - P 
= 4375 × (262/252) - 4375 
= 4732 - 4375 
= 357 taka 

difference = 357 - 350 tk 
= 7 tk.
৭১.
A man deposits Tk. 500 in a Bank at 10% interest rate compounded annually. At the end of the second year, the total amount including interest will become?
  1. ক
    ক) Tk. 595
  2. খ
    খ) Tk. 605
  3. গ
    গ) Tk. 690
  4. ঘ
    ঘ) Tk. 625
ব্যাখ্যা
Question: A man deposits Tk. 500 in a Bank at 10% interest rate compounded annually. At the end of the second year, the total amount including interest will become?

Solution: 
Given,
Principal, P = 500 Tk.
Rate of interest, r = 10% = 10/100 = 1/10
Time, n = 2 years.

We know,
Compound Amount = P (1 + r)n
= 500 × (1 + 1/10)2
= 500 × (11/10)2
= 500 × (11/10) × (11/10)
= 605
৭২.
How long will it take a sum of money invested at 5% per annum simple interest to increase its value by 20%?
  1. ক
    ক) 4 years
  2. খ
    খ) 5 years
  3. গ
    গ) 8 years
  4. ঘ
    ঘ) 10 years
ব্যাখ্যা
Question: How long will it take a sum of money invested at 5% per annum simple interest to increase its value by 20%?

Solution:
Let the principal (p) be 100 Tk
So, Interest, I = 100 × 20% = 20 Tk
and Interest, r = 5% = 5/100 = 1/20
Time, n = ?

ATQ, 
I = pnr
⇒ n = I/pr
⇒ n = (20 × 20)/100 = 4
৭৩.
If a sum of Tk. 9 is lent to be paid back in 10 equal monthly installments of Tk. 1 each, the rate of interest is -
  1. ক
    ক) 11%
  2. খ
    খ) 26.67%
  3. গ
    গ) 11.33%
  4. ঘ
    ঘ) 266.67%
ব্যাখ্যা

Let the rate of interest be R%
Amount due in 10 months
= 9 + simple interest on Tk. 9 for ten months
= 9 + {9 × R × (10/12)}/100
= 9 + (3R/40)
With the formula mentioned,
1 = 100{9 + 3R/40)}/[(100 × 10) + {R × 10(10 - 1)/(2 × 21)}]
900 + (15R/2) = 1000 + (15R/4)
15R/4 = 100
R = 26.67.
Hence the interest rate is 26.67%.

৭৪.
If the simple interest on Tk. X at X% per annum for 5 years is Tk. X, what is the value of X?
  1. ক
    12.5
  2. খ
    10
  3. গ
    20
  4. ঘ
    25
  5. ঙ
    50
ব্যাখ্যা

Question: If the simple interest on Tk. X at X% per annum for 5 years is Tk. X, what is the value of X?

Solution:
Given,
P = X
r = X% = X/100
n = 5 years
I = X

We know,
I = Prn
⇒ X = X × (X/100) × 5
⇒ X = X × (X/20)
∴ X = 20

৭৫.
A sum was put at simple interest at a certain rate for 3 years. Had it been put at 1% higher rate, it would have fetched 510 taka more. The sum is - 
  1. ক
    ক) Tk 15,000
  2. খ
    খ) Tk 16,000
  3. গ
    গ) Tk 17,000
  4. ঘ
    ঘ) Tk 20,000
ব্যাখ্যা
Questoin: A sum was put at simple interest at a certain rate for 3 years. Had it been put at 1% higher rate, it would have fetched 510 taka more. The sum is - 

Solution: 
Let the sum be Tk x and original rate be R%
Then, ((x × (R +1) × 3)/100) - {(x × R × 3)/100} = 510
⇒ 3Rx + 3x - 3Rx = 51000
⇒ 3x = 51000
⇒ x = 17000

Hence, sum = Tk 17,000
৭৬.
A certain sum of money becomes three times of itself in 20 years at simple interest. In how many years does it become double of itself at the same rate of simple interest?
  1. ক
    ক) 5 years
  2. খ
    খ) 10 years
  3. গ
    গ) 12 years
  4. ঘ
    ঘ) 15 years
ব্যাখ্যা

Let Principle = P.
Then, S.I = 2P and T = 20 years
∴ Rate = {(100 × 2P)/(P × 10)}
Now, principle = P, S.I. = P, R = 10%

∴ Time = {(100 × P)/(P × 10)} yrs
= 10 yrs.

৭৭.
A 15% stock yields 12.5%. What is the market value of the stock?
  1. ক
    Tk. 110
  2. খ
    Tk. 120
  3. গ
    Tk. 125.5
  4. ঘ
    Tk. 130
ব্যাখ্যা

Question: A 15% stock yields 12.5%. What is the market value of the stock?

Solution:
Earn Tk. 12.5 when market value = Tk. 100
Earn Tk. 1 when market value = Tk. (100 / 12.5)
Earn Tk. 15 when market value = Tk. (100 × 15)/12.5
= 1500/12.5
= 120

∴ The market value of the stock is Tk. 120.

৭৮.
A person borrows Tk. 5,000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 25/4 % per annum for 2 years. Find his gain in the transaction per year.
  1. ক
    ক) Tk. 112.50
  2. খ
    খ) Tk. 167.50
  3. গ
    গ) Tk. 150
  4. ঘ
    ঘ) Tk. 225
ব্যাখ্যা
Gain in 2 years = (5000 × 25/4 × 2/100) - (5000 × 4 × 2/100) = Tk. 225
Gain in 1 year = Tk. 225/2 = Tk. 112.5
৭৯.
A man deposits a certain amount in a bank under a scheme offering 7% annual simple interest. After 3 years, he receives 6655 taka in total. How much did he originally deposit?
  1. ক
    Tk. 5000
  2. খ
    Tk. 5050
  3. গ
    Tk. 5500
  4. ঘ
    Tk. 6150
ব্যাখ্যা
Question: A man deposits a certain amount in a bank under a scheme offering 7% annual simple interest. After 3 years, he receives 6655 taka in total. How much did he originally deposit?

Solution:
৮০.
A sum of money amounts to Tk. 735 in 3 years and Tk. 815 in 4 year. What's the sum?
  1. ক
    ক) Tk. 545
  2. খ
    খ) Tk. 395
  3. গ
    গ) Tk. 495
  4. ঘ
    ঘ) Tk. 595
ব্যাখ্যা
Question: A sum of money amounts to Tk. 735 in 3 years and Tk. 815 in 4 year. What's the sum?

Solution: 
Simple interest for 1 years = Tk. (815 - 735)
= Tk. 80
∴ Simple interest for 3 years = Tk.(80 × 3)
= Tk. 240

∴ Sum = (735 - 240)
= Tk. 495
৮১.
Lamia owns a hairdressing salon. She borrows Tk. 2,500 from a bank to improvements to her beauty salon. She is charged 4.5% per year compound interest. She pays the money back after 3 years. Calculate the total amount Lamia must pay to the bank.
  1. ক
    ক) Tk. 2852.92
  2. খ
    খ) Tk. 2528.29
  3. গ
    গ) Tk. 2752.29
  4. ঘ
    ঘ) Tk. 2679.92
ব্যাখ্যা
Question: Lamia owns a hairdressing salon. She borrows Tk. 2,500 from a bank to improvements to her beauty salon. She is charged 4.5% per year compound interest. She pays the money back after 3 years. Calculate the total amount Lamia must pay to the bank.

Solution: 
এখানে,
P = 2500 টাকা
r = 4.5%, = 4.5/100 = 45/1000 = 
n = 3 বছর

চক্রবৃদ্ধি মলধন C = P (1 + r)n
= 2500(1 + 45/1000)3
= 2500 × (1045/1000)3
= 2500 × 1.141
= 2852.92
৮২.
What will be the difference between simple and compound interest at 10% on a sum of TK. 5000 after 5 years?
  1. ক
    ক) 45
  2. খ
    খ) 152
  3. গ
    গ) 252
  4. ঘ
    ঘ) 552
ব্যাখ্যা

Simple interest, I = pnr = 5000 × 5 × 10/100
= 2500 taka
Compound interest = Amount − Principal
Amount = 5000(1 + 10/100)5 = 8052.55
So, compound interest = 8052.55 - 5000 = 3052.55

∴ Difference = 3052.55 - 2500 = 552.55 ≅ 552 taka

৮৩.
The stock he bought which was 6% of face value now worth 8% of the market value.
  1. ক
    ক) Tk. 84
  2. খ
    খ) Tk. 87
  3. গ
    গ) Tk. 95
  4. ঘ
    ঘ) Tk. 92
  5. ঙ
    ঙ) Tk. 75
ব্যাখ্যা

Let x be the market value,
we don't know face value so consider 100.
6% of 100 = 8% of x.
(6/100) × 100 = (8/100) × x.
6 = 8x/100.
x = 600/8.
x = 75.

Alternative Solution:
For an income of Tk. 8, investment = Tk. 100.
For an income of Tk. 6, investment = Tk.(100/8 × 6) = Tk. 75
Market value of Tk. 100 stock = Tk. 75.

৮৪.
Which is the better investment: 9% stock at Tk 90 or 12% stock at Tk 120?
  1. ক
    9% stock at Tk 90
  2. খ
    12% stock at Tk 120
  3. গ
    Both are same
  4. ঘ
    Cannot say
ব্যাখ্যা
Question: Which is the better investment: 9% stock at Tk 90 or 12% stock at Tk 120?

Solution:
→ Yield of 9% stock = (9 / 90) × 100 = 10%
→ Yield of 12% stock = (12 / 120) × 100 = 10%
On every taka you put in, both give the same 10 % return.
correct answer: Both are same
৮৫.
What is the ratio of simple interest earned on a certain amount at the rate of 12% p.a. for 9 years and that for 12 years?
  1. ক
    1 : 2
  2. খ
    3 : 4
  3. গ
    2 : 5
  4. ঘ
    7 : 9
ব্যাখ্যা

Question: What is the ratio of simple interest earned on a certain amount at the rate of 12% p.a. for 9 years and that for 12 years?

Solution: 
As the amount and interest rate are the same, 
Ratio = 9/12
= 3/4


৮৬.
What is the annual interest rate on an account that earns Tk. 948 in simple interest over 36 months with an initial deposit of Tk. 7900?
  1. ক
    ক) 40%
  2. খ
    খ) 4%
  3. গ
    গ) 3%
  4. ঘ
    ঘ) 3.3%
ব্যাখ্যা
We know, I = pnr
Or, r = I/pn = 948/(7900 × 36/12)
Or, r = 0.04 = 4/100 = 4%
৮৭.
Hannan invested an amount of Tk. 5000 in a fixed deposit scheme for 2 years at compound interest rate 5 p.c.p.a. How much amount will Hannan get on maturity of the fixed deposit?
  1. ক
    ক) Tk 5152.5
  2. খ
    খ) Tk. 5512.5
  3. গ
    গ) Tk. 5522.5
  4. ঘ
    ঘ) Tk. 5535.5
ব্যাখ্যা
Amount
= 5000 (1 + 5/100)2
= 5000 ×(1.05)2
= 5000 × 1.1025
= 5512.5
৮৮.
A man invested Tk. 14400 in tk. 100 shares of a company at 20% premium. If the company declares 5% dividend at the end of the year, then how much does he get?
  1. ক
    ক) 500
  2. খ
    খ) 600
  3. গ
    গ) 650
  4. ঘ
    ঘ) 720
ব্যাখ্যা

Number of shares = (14400/120) = 120
Face value = (100 × 120) = 12000
Annual income = (5/100 × 12000) = 600

৮৯.
Interest obtained on a sum of Tk 6250 for 5 years is Tk 1250. Find the rate of interest.
  1. ক
    ক) 4%
  2. খ
    খ) 5%
  3. গ
    গ) 6%
  4. ঘ
    ঘ) 10%
ব্যাখ্যা
Question: Interest obtained on a sum of Tk 6250 for 5 years is Tk 1250. Find the rate of interest.

Solution:
We know,
I = Pnr
⇒ r = I/pn
⇒ r = 1250/(5 × 6250)
⇒ r = (1250 × 100)/(5 × 6250)
⇒ r = 4%
৯০.
What would be the annual interest accrued on a deposit of Tk. 10000 in a bank that pays a 4.5% per annum rate of simple interest?
  1. ক
    Tk. 450
  2. খ
    Tk. 900
  3. গ
    Tk. 4500
  4. ঘ
    Tk. 45
ব্যাখ্যা
Question: What would be the annual interest accrued on a deposit of Tk. 10000 in a bank that pays a 4.5% per annum rate of simple interest?

Solution: 
Here,
P = 10000,
R = 4.5%,
T = 1

∴ SI = P × R × T/100
⇒ SI = 10000 × 4.5 × 1/100
⇒ SI = 450
Thus, the annual interest would be Tk. 450
৯১.
Mr. Karim deposited a certain amount of money for a fixed period of time. On maturity, he received a total of Tk. 50,000 when the ratio of interest and investment became 1: 4. If the simple interest rate was 5%, calculate the time period for which the money was invested.
  1. ক
    3 years
  2. খ
    4 years
  3. গ
    5 years
  4. ঘ
    8 years
  5. ঙ
    10 years
ব্যাখ্যা

Question: Mr. Karim deposited a certain amount of money for a fixed period of time. On maturity, he received a total of Tk. 50,000 when the ratio of interest and investment became 1: 4. If the simple interest rate was 5%, calculate the time period for which the money was invested.

Solution:
প্রদত্ত তথ্য অনুযায়ী, আসল এবং সুদের অনুপাত = 4 : 1
মোট প্রাপ্ত টাকা = 50,000 টাকা
মোট অনুপাত = 4 + 1 = 5
সুতরাং, আসল = 50,000 টাকার (4/5) অংশ = 40,000 টাকা
এবং, সুদ = 50,000 টাকার (1/5) অংশ = 10,000 টাকা

এখানে,
I = সুদ = 10,000 টাকা
P = আসল = 40,000 টাকা
R = সুদের হার = 5%
T = সময়কাল = ?

আমরা জানি, সরল সুদের ক্ষেত্রে,
I = (P × R × T)/100
⇒ 10,000 = (40,000 × 5 × T)/100
⇒ 10,000 = 400 × 5 × T
⇒ 10,000 = 2,000 × T
⇒ T = 10,000/2,000
⇒ T = 5

সুতরাং, টাকাটি 5 বছরের জন্য বিনিয়োগ করা হয়েছিল।

৯২.
As a salesperson, Poly can choose one of two methods of annual payment either an annual salary of Tk. 35,000 with no commission or an annual salary of Tk. 10,000 plus a 20 percent commission on her total annual sales. What must her total annual sales be to give her the same annual pay with either method?
  1. ক
    ক) Tk. 100,000
  2. খ
    খ) Tk. 120,000
  3. গ
    গ) Tk. 125,000
  4. ঘ
    ঘ) Tk. 130,000
ব্যাখ্যা
Let, total annual sales Tk. x
Therefore, 
20% of x + 10,000 = 35,000
or, 20x/100 = 35,000 - 10,000
or, x/5 = 25,000
or, x = 125,000
৯৩.
What will be the difference between simple and compound interest at 5% on a sum of Tk. 8000 after 2 years?
  1. ক
    Tk. 20
  2. খ
    Tk. 25
  3. গ
    Tk. 32
  4. ঘ
    Tk. 50
ব্যাখ্যা

Question: What will be the difference between simple and compound interest at 5% on a sum of Tk. 8000 after 2 years?

Solution:

দেওয়া আছে,
Principal, P = 8000 টাকা
Rate of interest, r = 5%
Time, n = 2 বছর

Simple Interest (SI):
SI = (P × r × n) / 100 = (8000 × 5 × 2) / 100 = 800 টাকা

Compound Interest (CI):
CI = P × (1 + r/100)n - P
= 8000 × (1 + 5/100)2 - 8000
= 8000 × (1.05)2 - 8000
= 8000 × 1.1025 - 8000
= 8820 - 8000 = 820 টাকা

∴ Difference between CI and SI:
= 820 - 800 = 20 টাকা

৯৪.
Which amount to be received after 4 years at the rate of 6% p.a of simple interest on a sum of Tk. 5700?
  1. ক
    Tk. 7068
  2. খ
    Tk. 6068
  3. গ
    Tk. 8250
  4. ঘ
    Tk. 7360
  5. ঙ
    None of these
ব্যাখ্যা
Question: Which amount to be received after 4 years at the rate of 6% p.a of simple interest on a sum of Tk. 5700?

Solution:
Given that,
Rate of interest, r = 6%
Principal, P = 5700
time, n = 4 years

∴ Simple interest, I = prn/100 
= (5700 × 6 × 4)/100
= 1368

So Total Amount = Principal + Simple interest = 5700 + 1368 = 7068 Tk
৯৫.
A corporation declares an annual dividend of 5%. Mugdho owns 500 shares (par value Tk. 80). How much dividend will he receive?
  1. ক
    Tk. 1500
  2. খ
    Tk. 1600
  3. গ
    Tk. 2000
  4. ঘ
    None of these
ব্যাখ্যা
Question: A corporation declares an annual dividend of 5%. Mugdho owns 500 shares (par value Tk. 80). How much dividend will he receive?

Solution:
Amount of total shares = 500 × 80 = Tk. 40000

From Tk. 100 Mugdho gets dividends Tk. 5
From Tk. 1 Mugdho gets dividends Tk. 5/100
From Tk. 40000 Mugdho gets dividends Tk. (5 × 40000)/100 
= Tk. 2000
৯৬.
If the simple interest on Tk. N at N% per annum for 5 years is Tk. N, what is the value of N?
  1. ক
    20
  2. খ
    25
  3. গ
    30
  4. ঘ
    15
ব্যাখ্যা

Question: If the simple interest on Tk. N at N% per annum for 5 years is Tk. N, what is the value of N?

Solution:
Given,
P = N
r = N% = N/100
n = 5 years
I = N

We know,
I = Prn
⇒ N = N × (N/100) × 5
⇒ N = (N2 × 5)/100
⇒ N = N2/20
⇒ N2 = 20N
⇒ N2/N = 20
∴ N = 20

সুতরাং, N এর মান হলো 20

৯৭.
If Tk. 5,000 is invested at 12% annual rate of interest, how much will the investment be worth after 2 years?
  1. ক
    ক) 5785
  2. খ
    খ) 6272
  3. গ
    গ) 7190
  4. ঘ
    ঘ) 8225
ব্যাখ্যা
প্রশ্ন: If Tk. 5,000 is invested at 12% annual rate of interest, how much will the investment be worth after 2 years?

সমাধান: 
দেওয়া আছে,
আসল, P = 5000 টাকা
মুনাফার হার, r = 12%
সময়, n = 2 বছর

প্রথম বছর,
মুনাফা I = Pnr = 5000 × 1 × 12% 
= 5000 × (12/100)
= 50 × 12
= 600 টাকা
∴ প্রথম বছর পর মোট টাকা = 5000 + 600 = 5600 টাকা

দ্বিতীয় বছর,
মুনাফা I = Pnr = 5600 × 1 × 12%
= 5600 × (12/100)
= 672 টাকা
∴ দ্বিতীয় বছর পর মোট টাকা = 5600 + 672 = 6272 টাকা

∴ দুই বছর পর মোট টাকা = 6272 টাকা।
৯৮.
Tk. 500 is deposited in a savings account which pays 7% annual interest compounded semi-annually. To the nearest Taka, how much is in the account at the end of the year?
  1. ক
    ক) 542
  2. খ
    খ) 536
  3. গ
    গ) 512
  4. ঘ
    ঘ) 524
ব্যাখ্যা
I = P(1+r)2
= 500{1 + 7/(2 × 100)}2
= 500 × (1 + 0.035)2
= 500 × (1.035)2
= 535.6125 ≅ 536
৯৯.
In how many years will Tk. 2000 amounts to Tk. 2420 at 10% per annum compound interest?
  1. ক
    2 years
  2. খ
    3 years
  3. গ
    4 years
  4. ঘ
    2.5 years
ব্যাখ্যা
Question: In how many years will Tk. 2000 amounts to Tk. 2420 at 10% per annum compound interest?

Solution: 
Principal = Tk. 2000
Amount = Tk. 2420
Rate = 10% 

We Know
C = P(1 + r)n
2420 = 2000(1 + 10/100)n
2420/2000 = (11/10)n
121/100 = (11/10)n
(11/10)2 = (11/10)n
n = 2
১০০.
There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of Tk.1400 after 3 years at the same rate?
  1. ক
    463.4 Tk.
  2. খ
    350.5 Tk.
  3. গ
    223.2 Tk.
  4. ঘ
    145.4 Tk.
ব্যাখ্যা
Question: There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of Tk.1400 after 3 years at the same rate?

Solution: 
Let P = Tk. 100.
Then, S.I. Tk. = 60 and n = 6 years

Rate =(100 × 60)/(100 × 6) = 10%

Now, P = Tk.. 1400.
n = 3 years and R = 10% p.a.

C.I. = 1400(1 + 10/100)3 - 1400
= 1400(1.1)3 - 1400
= 1863.4 - 1400
= 463.4