Simple and Compound Interest, Stock

PrepBank · পাতা ৫ / ৯ · ৪০১–৫০০ / ৮৫৮

৪০১.

Rakib charges at 7% P.A. simple interest to Maruf and Sunny and lends a certain amount to Sunny and Tk. 2500 to Maruf. After 4 years, Rakib completely receives Tk. 1120 as interest from Maruf and Sunny. Find the amount lent to Sunny?

ক
ক) Tk. 3000
খ
খ) Tk. 1500
গ
গ) Tk. 900
ঘ
ঘ) Tk. 1600

ব্যাখ্যা

Question: Rakib charges at 7% P.A. simple interest to Maruf and Sunny and lends a certain amount to Sunny and Tk. 2500 to Maruf. After 4 years, Rakib completely receives Tk. 1120 as interest from Maruf and Sunny. Find the amount lent to Sunny?

Sulotion:
Let,
Rakib lent Sunny Tk. x,
∴ Rakib lent total Tk. (x + 2500)

We know that,
Interest, I = Pnr
∴ 1120 = (x + 2500) × 4 × (7/100)
⇒ 112000 = (x + 2500) × 28
⇒ x + 2500 = 112000/28
⇒ x + 2500 = 4000
⇒ x = 4000 - 2500
∴ x = 1500

∴ Rakib lent Sunny Tk. 1500

৪০২.

A sum earns Tk. 1260 more interest in 8 years than in 5 years at 7.5% simple interest. Calculate the principal.

ক
Tk. 5000
খ
Tk. 6000
গ
Tk. 6250
ঘ
Tk. 5600

ব্যাখ্যা

Question: A sum earns Tk. 1260 more interest in 8 years than in 5 years at 7.5% simple interest. Calculate the principal.

Solution:
Given that,
Rate, r = 7.5% per annum
Extra interest earned in, n = (8 - 5) = 3 years
SI = Tk. 1260

We know,
Simple Interest,
SI = (P × r × n) / 100
⇒ 1260 = (P × 7.5 × 3) / 100
⇒ 1260 = (P × 22.5) / 100
⇒ 1260 × 100 = 22.5 × P
⇒ 126,000 = 22.5 × P
⇒ P = 126000/22.5
∴ P = 5600

So the principal is Tk. 5600

৪০৩.

A sum of Tk. 12,500 amounts to Tk. 15,500 in 4 year at the rate of simple interest. What is the rate of interest?

ক
ক) 3%
খ
খ) 4%
গ
গ) 5%
ঘ
ঘ) 6%

ব্যাখ্যা

S.I.=Tk.(15500−12500)=Tk.3000
Rate=(100×3000)/(12500×4)%= 6%

৪০৪.

For how much money will the profit at the rate of Tk. 5 per annum in 2 years 6 months be same as that of Tk. 1000 at the rate of Tk. 6 per annum in 4 years?

ক
Tk. 1850
খ
Tk. 1790
গ
Tk. 1840
ঘ
Tk. 1920

ব্যাখ্যা

Question: For how much money will the profit at the rate of Tk. 5 per annum in 2 years 6 months be same as that of Tk. 1000 at the rate of Tk. 6 per annum in 4 years?

Solution:
Here are 2 parts,

In one part,
Given,
Principal P = Tk. 1000
Rate r = 6 per annum
Time n = 4 years

So simple interest I = (P × r × n)
= (1000 × 6/100 × 4)
= 240

In the other part,
I = Tk. 240
r = 5% = 1/20
n = 2 years 6 months
= 2.5 years

∴ P = I/rn
= 240/(1/20 × 2.5)
= (240 × 20)/(1 × 2.5)
= (4800 × 10)/25
= Tk. 1920

৪০৫.

A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay. Tk. 5,400 interest only for the period, The principal amount borrowed by him was:

ক
ক) Tk. 20,000
খ
খ) Tk. 10,000
গ
গ) Tk. 2,000
ঘ
ঘ) Tk. 15,000

ব্যাখ্যা

এখানে,
মুনাফার হার r = 12%= 12/100
সময় n = 3 বছর
মুনাফা I = 5400 টাকা

আসল P =?

আমরা জানি
I = Pnr
5400 = P × 3 × (12/100)
P = (5400 × 100)/(3 × 12)
P = 15000

৪০৬.

A sum of money at simple interest amounts to TK. 5700 in 2 years and Tk. 6750 in 5 years at the rate of -

ক
ক) 4%
খ
খ) 7%
গ
গ) 5%
ঘ
ঘ) 6%

ব্যাখ্যা

S.I. in 3 years = 6750 - 5700 = 1050
Interest every year = 1050/3 = 350
So, principal = 5700 - 2 × 350 = 5000

We know, I = pnr
Or, Interest rate, r = I/pn
= 700/(5000×2) × 100
= 7%

৪০৭.

The compound interest on a certain sum for 2 years at 5% per annum is Tk. 820. The simple interest on the same sum for half the time at double the rate percent per annum is:

ক
Tk. 720
খ
Tk. 750
গ
Tk. 800
ঘ
Tk. 860

ব্যাখ্যা

প্রশ্ন: The compound interest on a certain sum for 2 years at 5% per annum is Tk. 820. The simple interest on the same sum for half the time at double the rate percent per annum is:

সমাধান:
দেওয়া আছে,
চক্রবৃদ্ধি সুদ (CI) = 820 টাকা
সময় (n) = 2 বছর
সুদের হার (r) = 5%
আমরা জানি,
CI = P(1 + r/100)ⁿ - P
820 = P(1 + 5/100)² - P
⇒ 820 = P(1.05)² - P
⇒ 820 = 1.1025P - P
⇒ 820 = 0.1025P
⇒ P = 820/0.1025
⇒ P = 8000 টাকা

এখন,
আসল (P) = 8000 টাকা
সময় (n) = অর্ধেক সময় = 2 ÷ 2 = 1 বছর
সুদের হার (r) = দ্বিগুণ সুদের হার = 5% × 2 = 10%
আমরা জানি,
SI = (P × r × n)/100
= (8000 × 10 × 1)/100
= (80000)/100
= 800 টাকা
∴ নির্ণেয় সরল সুদ হলো 800 টাকা।

৪০৮.

A sum of Tk 7800 gives a simple interest of Tk. 702 in 2 years and 3 months. The rate of interest per annum is =?

ক
3%
খ
4%
গ
5%
ঘ
6%

ব্যাখ্যা

Question: A sum of Tk 7800 gives a simple interest of Tk. 702 in 2 years and 3 months. The rate of interest per annum is =?

Solution:
Time = 2 years 3 months
= 2 + 3/12 = 2 + 1/4 = (8 + 1)/4
= 9/4 years

Here,
I = Tk. 702, P = Tk. 7800
n = 9/4 years
r = ?

We know,
I = Pnr
⇒ r = I/pn
⇒ r = (702 × 4 × 100)/(7800 × 9)
∴ r = 4%

৪০৯.

The present value of a machine is Tk. 10000 and its value depreciates every year by 10%. What will be its value after 2 years?

ক
ক) 7500
খ
খ) 7300
গ
গ) 9200
ঘ
ঘ) 9700
ঙ
ঙ) 8100

ব্যাখ্যা

If the value of the machine at the beginning of year 1 is 10,000 and then it reduces by 10%, the value of the machine at the end of year 1 is:
10,000 × (100%-10%) = 9,000
And again, at the end of Year 2, we follow a similar route:
9000 × (100% - 10%)
= 8,100

৪১০.

How long will it take for an amount of taka 450 to yield taka 81 as interest at 4.5% per annum of simple interest?

ক
ক) 4 years
খ
খ) 4.5 years
গ
গ) 5 years
ঘ
ঘ) 5.5 years

ব্যাখ্যা

সরল মুনাফার ক্ষেত্রে,
I = Pnr
Or, 81 = (450 × n × 4.5)/100
Or, n = (81 × 100) / (450 × 4.5)
= 4 বছর

৪১১.

If Tk. 3000 is loaned for 4 months at a 4.5% annual rate, how much interest is earned?

ক
Tk. 135
খ
Tk. 120
গ
Tk. 60
ঘ
Tk. 50
ঙ
Tk. 45

ব্যাখ্যা

Question: If Tk. 3000 is loaned for 4 months at a 4.5% annual rate, how much interest is earned?

Solution:
P = 3000
n = 4 months = 4/12 years = 1/3 year
r = 4.5%

I = Pnr
= {3000 × (1/3) × (4.5)}/100
= 45

৪১২.

The present of Tk.169 due in 2year at 4% per annum compound interest is

ক
ক) Tk.150.50
খ
খ) Tk.154.75
গ
গ) Tk.156.25
ঘ
ঘ) Tk.158

ব্যাখ্যা

Present worth = 169/(1+4/100)^n = 156.25

৪১৩.

Rita invested equal amounts at 5% and 7% simple interest for 4 years. If she received total interest of Tk. 1920, what was the amount invested in each scheme?

ক
Tk. 3500
খ
Tk. 4000
গ
Tk. 4500
ঘ
Tk. 5000

ব্যাখ্যা

Question: Rita invested equal amounts at 5% and 7% simple interest for 4 years. If she received total interest of Tk. 1920, what was the amount invested in each scheme?

Solution:
Let the amount invested in each scheme = x taka
So, same amount at 5% and same amount at 7%

Interest at 5% for 4 years,
I₁ = (x × 5 × 4)/100
= 20x/100
= x/5
= 0.20x

And, Interest at 7% for 4 years,
I₂ = (x × 7 × 4)/100
= 28x/100
= 0.28x

Total interest received = I₁ + I₂
0.20x + 0.28x = 1920
⇒ 0.48x = 1920
⇒ x = 1920/0.48
⇒ x = 1920 × (100/48)
⇒ x = 1920 × (25/12)
⇒ x = 160 × 25
∴ x = 4000

So, the amount invested in each scheme Tk. 4000

৪১৪.

Find the rate of interest if the amount after 2 years of simple interest on a capital of tk 1200 is tk 1680.

ক
20%
খ
16%
গ
10%
ঘ
12%
ঙ
None of these

ব্যাখ্যা

Question: Find the rate of interest if the amount after 2 years of simple interest on a capital of tk 1200 is tk 1680.

Solution:
given,
Principal, P = 1200 taka
Time, n = 2
Interest, I = 1680 - 1200 = 480
Rate of interest, r = ?

We know that,
I = pnr
⇒ 480 = (1200 × 2 × r)/100
⇒ 480 = 2400 × r/100
⇒ 480 = 24 × r
⇒ r = 480/24
∴ r = 20

So, the rate of interest is 20%

৪১৫.

In how many years the compound interest on Tk. 10000 at the rate of 10% will be Tk. 2100?

ক
1.5 years
খ
2 years
গ
2.5 years
ঘ
3 years

ব্যাখ্যা

Question: In how many years the compound interest on Tk. 10000 at the rate of 10% will be Tk. 2100?

Solution:
P = 10000
r = 10% = 10/100 = 1/10 = 0.1
compound principal C = 10000 + 2100 = 12100
time = n years

C = P(1 + r)ⁿ
⇒ 12100 = 10000(1 + 0.1)ⁿ
⇒ 12100/10000 = (1.1)ⁿ
⇒ 121/100 = (11/10)ⁿ
⇒ (11/10)² = (11/10)ⁿ
∴ n = 2

৪১৬.

If a sum of taka invested amount to BDT 460 in 3 years and amounts to BDT 500 in 5 years then what is the invested sum in BDT?

ক
ক) 300
খ
খ) 350
গ
গ) 400
ঘ
ঘ) 450
ঙ
ঙ) None

ব্যাখ্যা

500 - 460 = 40, interest of two years
So, interest for three year is (40×3)/2 = 60 tk
∴ Initial investment = 460 - 60 = 400 tk

৪১৭.

Nazrul borrowed some money for 240 days. He asked the banker for the money and the banker charged Tk. 720 as simple interest at 6% per annum. What was the amount he borrowed?

ক
Tk. 12000
খ
Tk. 15000
গ
Tk. 16000
ঘ
Tk. 18000

ব্যাখ্যা

Question: Nazrul borrowed some money for 240 days. He asked the banker for the money and the banker charged Tk. 720 as simple interest at 6% per annum. What was the amount he borrowed?

Solution:
এখানে
সময়, n = 240 দিন
= 8 মাস
= 8/12 বছর
= 2/3 বছর

মুনাফা, I = 720 টাকা
মুনাফার হার, r = 6% = 6/100
আসল, P = ?

আমরা জানি
I = Pnr
⇒ Pnr = I
⇒ P = I/(nr)
= 720/{(2/3) × (6/100)}
=720/(1/25)
= 720 × 25
= 18000 টাকা

৪১৮.

The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Tk. 1. The sum (in Tk.) is-

ক
625
খ
630
গ
640
ঘ
650

ব্যাখ্যা

Question: The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Tk. 1. The sum (in Tk.) is-

Solution:
Let the sum be Rs. x. Then,

Compound Interest = x(1 + 4/100) ²- x
= (676/625)x - x
= (51/625)x

Simple Interest = x × 2 × 4/100
= (2/25)x

ATQ,
(51/625)x - (2/25)x = 1
⇒ {(51 - 50)/625}x = 1
⇒ x/625 = 1
∴ x = 625

৪১৯.

Find the compound interest after 2 years on Tk. 14000 at the rate of interest 5% per annum.

ক
Tk. 15435
খ
Tk. 15400
গ
Tk. 1455
ঘ
Tk. 1400
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

৪২০.

If the difference between the simple interest and compound interests on some principal amount at 20% for 3 years is Tk. 48, then the principal amount is -

ক
ক) Tk. 375
খ
খ) Tk. 325
গ
গ) Tk. 365
ঘ
ঘ) Tk. 395

ব্যাখ্যা

Let the sum be Tk. x
Amount after 3 years on Tk. x at 20% per annum when interest is compounded annually
P(1 + R/100)^T
= x{1 + (20/100)}³
= x(120/100)³
= x(6/5)³
Compound interest = {x(6/5)³ - x}
= x{(6/5)³ - 1}
= x{(216/125) - 1}
= 91x/125
Simple interest PRT/100 = (x × 20 × 3)/100
= 3x/5
Given that difference between compound interest and simple interest is Tk. 48
(91x/125) - (3x/5) = 48
⇒ (91x - 75x)/125 = 48
⇒ 16x/125 = 48
⇒ x = (48 × 125)/16
= 3 × 125
= Tk. 375.

৪২১.

An amount has increased by 80% over 16 years at simple interest. What is the compound interest on Tk. 12,000 after two years at the same rate?

ক
Tk. 13230
খ
Tk. 13320
গ
Tk. 12320
ঘ
Tk. 1230

ব্যাখ্যা

Question: An amount has increased by 80% over 16 years at simple interest. What is the compound interest on Tk. 12,000 after two years at the same rate?

Solution:
Let,
simple interest r%

I = pnr/100
⇒ I/p = nr/100
⇒ 0.8 = 16r/100
⇒ 8/10 = 16r/100
∴ r = 5%

The compound interest = 12000 (1+5/100)² - 12000
= 12000 × 105/100 × 105/100 - 12000
= 12000 × 21/20 × 21/20 - 12000
= 12000 × 441/400 - 12000
= 13230 - 12000
= Tk. 1230

৪২২.

A sum of money doubles itself in 8 years at a certain rate of simple interest. In how many years will it become four times itself at the same rate of interest?

ক
12 years
খ
24 years
গ
32 years
ঘ
20 years

ব্যাখ্যা

Question: A sum of money doubles itself in 8 years at a certain rate of simple interest. In how many years will it become four times itself at the same rate of interest?

Solution:
Given that,
The sum doubles itself in 8 years.
Amount after 8 years = 2P
Simple Interest for 8 years = P

We know,
SI = (P × r × n)/100
⇒ P = (P × r × 8)/100
⇒ 8r = 100
⇒ r = 100/8
∴ r = 12.5% per year

Now, we want to find in how many years the sum becomes four times itself.
Amount = 4P
Interest needed = 4P - P = 3P

We know,
SI = (P × r × n)/100
⇒ 3P = (P × 12.5 × n)/100. ; [r = 12.5%]
⇒ 3 = (12.5 × n)/100
⇒ n = (3 × 100)/12.5
∴ n = 24 years

∴ The sum will become four times itself in 24 years.

৪২৩.

If you deposit 10,000 tk in a bank at 5% interest rate, compound interest for 6 months, what will be the total profit in 2 years?

ক
1038.13 Tk.
খ
12028 Tk.
গ
13026.28 Tk.
ঘ
12015.36 Tk.

ব্যাখ্যা

Question: If you deposit 10,000 tk in a bank at 5% interest rate, compound interest for 6 months, what will be the total profit in 2 years?

Solution:
Given, p = 10,000; n = 2; m = 2
r = 5/(100 × 2) = 1/40

Now,
C = p[1 + {r/(100 × m)}]^{n × m}
= 10000[1 + {5/(100 × 2)}^{2 × 2}
= 10000{1 + (1/40)}⁴
= 10000(41/40)⁴
= 10000 × (41/40) × (41/40) × (41/40) × (41/40)
= (41/4) × (41/4) × (41/4) × (41/4)
= 2825761/256
= 11038.13 Tk.
profit = (11038.13 - 10000) Tk.
= 1,038.128 Tk.

৪২৪.

A sum of money is borrowed and paid back in two annual instalments of Tk. 882 each allowing 5% compound interest. The sum borrowed was -

ক
ক) Tk. 1620
খ
খ) Tk. 1640
গ
গ) Tk. 1680
ঘ
ঘ) Tk. 1700

ব্যাখ্যা

Principle,
= (P.W. of Tk. 882 due 1 year hence) + (P.W of Tk. 882 due 2 years hence)
= [{882/(1 + 5/100)} + {882/(1 + 5/100)²}]
= [{(882 × 20)/21} + {(882 × 400)/441}]
= Tk. 1640.

৪২৫.

A man lends Tk. 5000 in three parts at different rates of simple interest per annum. If he gets 4% on TK. 1500 and 5% on TK. 2500, what percent must he get for the remainder, if the average rate of simple interest per annum is 5.5%?

ক
5%
খ
7.5%
গ
9%
ঘ
12%

ব্যাখ্যা

Question: A man lends Tk. 5000 in three parts at different rates of simple interest per annum. If he gets 4% on TK. 1500 and 5% on TK. 2500, what percent must he get for the remainder, if the average rate of simple interest per annum is 5.5%?

Solution:
Total Principal, P = 5000 TK.
Average Interest Rate = 5.5%
Total Interest required = (5000 × 5.5)/100 = 275 TK.

Interest from 1st part (1500 at 4%) = (1500 × 4)/100 = 60 TK.
Interest from 2nd part (2500 at 5%) = (2500 × 5)/100 = 125 TK.

Total interest from these two parts = 60 + 125 = 185 TK.
Remaining Interest needed = 275 - 185 = 90 TK.

Remaining Principal = 5000 - (1500 + 2500) = 1000 TK.

Let the required rate for the remainder be r%.
Using SI = Pnr/100 (where n = 1 year):
⇒ 90 = (1000 × 1 × r)/100
⇒ 90 = 10r
⇒ r = 90/10
⇒ r = 9

So, he must get 9% interest for the remainder.

৪২৬.

How much time will it take for an amount of Tk. 1800 to yield Tk. 81 as interest at 9% per annum of simple interest?

ক
18 months
খ
12 months
গ
6 months
ঘ
4 months
ঙ
None

ব্যাখ্যা

Question: How much time will it take for an amount of Tk. 1800 to yield Tk. 81 as interest at 9% per annum of simple interest?

Solution:
I = Pnr
⇒ 81 = 1800 × n × (9/100)
⇒ n = (81 × 100)/(1800 × 9)
∴ n = 1/2 year = 6 months

৪২৭.

A sum of Tk 7800 gives a simple interest of Tk. 702 in 2 years and 3 months. The rate of interest per annum is =?

ক
ক) 2%
খ
খ) 4%
গ
গ) 5%
ঘ
ঘ) 8%

ব্যাখ্যা

Question: A sum of Tk 7800 gives a simple interest of Tk. 702 in 2 years and 3 months. The rate of interest per annum is =?

Solution:
Time = 2 years 3 months
= 2 + 3/12
= 2 + 1/4
= (8+1)/4
= 9/4 years

Here,
I = 702
P = 7800
n = 9/4
r = ?

We know,
I = Pnr
⇒ r = I/pn
⇒ r = (702 × 4 × 100)/(7800 × 9)
⇒ r = 4%

৪২৮.

A sum of money at simple interest amounts to Tk. 715 in 4 years and to Tk. 754 in 5 years. The sum is:

ক
500 tk.
খ
559 tk.
গ
600 tk.
ঘ
620 tk.

ব্যাখ্যা

Question: A sum of money at simple interest amounts to Tk. 715 in 4 years and to Tk. 754 in 5 years. The sum is:

Solution:
১ বছরের সুদ = ৭৫৪ - ৭১৫ টাকা
= ৩৯ টাকা

∴ ৪ বছরে সুদ = (৩৯ × ৪) টাকা
= ১৫৬ টাকা

∴ আসল = ৭১৫ - ১৫৬ টাকা
= ৫৫৯ টাকা

৪২৯.

A total of TK. 1200 was deposited in two saving accounts for one year, one portion at 5% simple interest, and the rest at 7% simple interest. If Tk. 72 was earned in interest, how much was deposited at 5%?

ক
Tk. 410
খ
Tk.520
গ
Tk. 600
ঘ
Tk. 650
ঙ
None of the above

ব্যাখ্যা

The amount of money deposited at 5% interest = x
The amount of money deposited at 7% = 1200 - x
A/Q, ( x × 5 × 1)/100 + {(1200 - x) × 7 × 1}/100 = 72
Or, 5x + 8400 - 7x = 7200
Or, 2x = 1200
So, x = 600

৪৩০.

A sum of money placed at compound interest doubles itself in 4 years. In how many years will it amount to 8 times?

ক
ক) 16 years
খ
খ) 14 years
গ
গ) 10 years
ঘ
ঘ) 12 years
ঙ
ঙ) 24 years

ব্যাখ্যা

Let,
Principal = Tk. 100
Amount = Tk. 200

Alternative Method:
Suppose 100 be the principal.
In 4 years it doubles and becomes 200.
In next 4 years 200 double to 400.
In next 4 years 400 doubles to 800.
Hence the period for 8 times is 12 years.

৪৩১.

The compound interest on Tk. 30000 at 7% per annum is Tk. 4347. The period is-

ক
2 years
খ
2.5 years
গ
3 years
ঘ
4 years

ব্যাখ্যা

Question: The compound interest on Tk. 30000 at 7% per annum is Tk. 4347. The period is-

Solution:

Amount = Tk. (30000 + 4347) = Tk. 34347

let the time be n years

Then,
30000(1 + 7/100)ⁿ = 34347

⇒ (107/100)ⁿ = 34347/30000 = 11449/10000 = (107/100)²
∴ n = 2 years

৪৩২.

The compound interest on a certain sum for 2 years at 10% per annum is Tk. 525 . The simple interest on the same sum for doubled the time at half the rate percent per annum is-

ক
ক) Tk. 450
খ
খ) Tk. 480
গ
গ) Tk. 500
ঘ
ঘ) Tk. 550

ব্যাখ্যা

Let the sum be Tk. P

Here
P(1 + 10/100)²- P = 525
or, P(110/100)² - P = 525
or, P(1.1)² - P = 525
or, P( 1.21 - 1) = 525
or, P × 0.21 = 525
or, p = 525/.21
P = 2500

Again
S.I = (2500 × 5 × 4)/100
= 500

৪৩৩.

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?

ক
ক) 5%
খ
খ) 10%
গ
গ) 15%
ঘ
ঘ) 20%

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

৪৩৪.

There is 90% increase in an amount in 9 years at simple interest. What will be the compound interest of Tk.15,000 after 4 years at the same rate?

ক
ক) 4533
খ
খ) 5497
গ
গ) 6962
ঘ
ঘ) 4965

ব্যাখ্যা

ধরি
আসল P =100 টাকা
সরল মুনাফা I = 100 এর 90%
= 90 টাকা
সময় n = 9 বছর

মুনাফার হার = r
আমরা জানি
I = Pnr
r = I/Pn
={(100 ×90)/(100 × 9)}% = 10%
আবার
আসল P = 15000
সময় n = 4 বছর
চক্রবৃদ্ধি মুনাফা = P(1 + r)ⁿ - P
= 15000{(1 + 1/10)⁴} - 15000
= 15000 ×1.4641 - 15000
= 21,961.5 - 15000
= 6,961.5
≈6,962

৪৩৫.

A sum of money becomes 6/5 of itself in 3 years at a certain rate of simple interest. The rate of interest per annum is-

ক
6.67%
খ
6.50%
গ
3.33%
ঘ
7.67%

ব্যাখ্যা

Question: A sum of money becomes 6/5 of itself in 3 years at a certain rate of simple interest. The rate of interest per annum is-

Solution:
Let principal = 5P
Hence amount = 5P × 6/5 = 6P
SI = 6P - 5P = P
Time = 3 years

SI = P × R × T/100
⇒ P = 5P × R × 3/100
⇒ R = 100/15
∴ R = 6.67%

৪৩৬.

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?

ক
ক) 8%
খ
খ) 10%
গ
গ) 12%
ঘ
ঘ) 14%

ব্যাখ্যা

৪৩৭.

Nuhi buys 1,000 shares of stock for the current stock price of 20 tk. per share. If the stock price goes up to 25 tk. per share, by what percentage does Nuhi increase his money?

ক
15%
খ
20%
গ
25%
ঘ
30%

ব্যাখ্যা

Question: Nuhi buys 1,000 shares of stock for the current stock price of 20 tk. per share. If the stock price goes up to 25 tk. per share, by what percentage does Nuhi increase his money?

Solution:
প্রতি শেয়ার ২০ টাকা হলে, মোট শেয়ার = ১০০০ × ২০ টাকা
= ২০০০০ টাকা

২৫ টাকা হলে মোট শেয়ার = ১০০০ × ২৫ টাকা
= ২৫০০০ টাকা

টাকা বৃদ্ধি পাবে = ২৫০০০ - ২০০০০ টাকা
= ৫০০০ টাকা

শতকরা বৃদ্ধি = (৫০০০/২০০০০) × ১০০%
= ২৫%

৪৩৮.

The rate at which a sum becomes four times of itself in 15 years at simple interest will be?

ক
ক) 18%
খ
খ) 20%
গ
গ) 22%
ঘ
ঘ) 23%

ব্যাখ্যা

Question: The rate at which a sum becomes four times of itself in 15 years at simple interest will be?

Solution:
Let, Sum = Tk. x.
Then, Simple interest, I = 4x - x = 3x.
We know,
I = Pnr
⇒ r = I/Pn
⇒ r = {(3x × 100)/(x × 15)}%
∴ r = 20%

৪৩৯.

Find the compound interest on Tk 1000 at the rate of 20% per annum for 18 month when interest is compounded half yearly.

ক
ক) Tk. 1331
খ
খ) Tk. 2337
গ
গ) Tk. 4320
ঘ
ঘ) Tk. 2325
ঙ
ঙ) Tk. 6370

ব্যাখ্যা

Given,Principal,P = tk. 1000
Compound rate,R = 20%per annum
= 20/2
= 10% half-yearly
Time = 18 month
= 3 half - years

Amount,A = {P × [1 + (R/100)]ⁿ}
= {1000 × [1 + (10/100)]³}
= (1000 × 11 × 11 × 11) ÷ (10 × 10 × 10)
A = tk.1331
Hence, compound interest = tk.1331

৪৪০.

A sum of Tk. 36,000 is invested at 8% per annum simple interest. Find the amount after 5 years.

ক
Tk. 14,400
খ
Tk. 44,400
গ
Tk. 50,400
ঘ
Tk. 54,400

ব্যাখ্যা

Question: A sum of Tk. 36,000 is invested at 8% per annum simple interest. Find the amount after 5 years.

Solution:
Principal, P = Tk. 36,000
Rate of interest, r = 8%
Time, n = 5 years

We know,
I = Pnr
⇒ I = 36,000 × 5 × 8/100
= 36,000 × 40/100
= 36,000 × 2/5
= Tk. 14,400

Amount, A = P + I
= 36,000 + 14,400
= Tk. 50,400

৪৪১.

What is the amount for a sum of money Tk. 7500 at 6% rate of interest compound interest for 2 years?

ক
Tk. 8427
খ
Tk. 8417
গ
Tk. 8400
ঘ
Tk. 8390

ব্যাখ্যা

Question: What is the amount for a sum of money Tk. 7500 at 6% rate of interest compound interest for 2 years?

Solution:
C = P(1 + r)ⁿ
= 7500(1 + 6/100)²
= 7500 × 1.06 × 1.06
= 8427

৪৪২.

A certain amount of money earning simple interest becomes 7/5^th of the initial amount in 4 years. What is the interest rate?

ক
10%
খ
8%
গ
6%
ঘ
4%

ব্যাখ্যা

Question: A certain amount of money earning simple interest becomes 7/5^th of the initial amount in 4 years. What is the interest rate?

Solution:
ধরি,
আসল P = 100 টাকা
মুনফা-আসল A = 100 এর 7/5
= 140 টাকা

মুনাফা I = 140 - 100 = 40 টাকা
সময় n = 4 বছর
মুনাফার হার r = ?

আমরা জানি,
I = Pnr
⇒ r = I/Pn
= (40 × 100)/(100 × 4)
= 10%

৪৪৩.

The difference between the simple interest received from two different sources on Rs. 1500 for 3 years is Rs. 13.50. The difference between their rates of interest is ?

ক
0.1%
খ
0.2%
গ
0.3%
ঘ
0.4%

ব্যাখ্যা

Let the rate of interest for two different sources is r₁ and r₂ respectively.

1500 × r₁ × 3/100 - 1500 × r₂ × 3/100 = 13.50
4500r₁ - 4500r₂ = 1350
(r₁ - r₂) = 1350/4500
Hence required difference in rates = 0.3%

৪৪৪.

Find the income on 7(½) % stock of Tk. 2000 purchased at Tk. 80.

ক
ক) TK.160
খ
খ) TK.148
গ
গ) TK.150
ঘ
ঘ) TK.109
ঙ
ঙ) TK. 125

ব্যাখ্যা

Face Value of the stock = Tk.2000
Dividend is 7(1/2)% = 15/2% of the face value
Dividend = (2000 × 15) ÷ (2 × 100)
= Tk. 150

৪৪৫.

A sum of Tk. 1000 was lent to two people, one at the rate of 5% and the other at the rate of 8%. If the simple interest after one year is Tk. 62, find the sum lent at 5% rate.

ক
Tk. 400
খ
Tk. 600
গ
Tk. 700
ঘ
Tk. 650

ব্যাখ্যা

Question: A sum of Tk. 1000 was lent to two people, one at the rate of 5% and the other at the rate of 8%. If the simple interest after one year is Tk. 62, find the sum lent at 5% rate.

Solution:
Let the sum lent at 5% be P.
∴ Sum lent at 8 % = 1000 - P

Now, according to the question,
SI for 5% + SI for 8% = 62
⇒ (P × 5 × 1/100) + ((1000 - P) × 8 × 1/100) = 62
⇒ 5P + 8(1000 - P) = 6200
⇒ 5P + 8000 - 8P = 6200
⇒ 3P = 1800
⇒ P = 600
Therefore, sum lent at 5 % = P = Tk. 600

৪৪৬.

Rakib invested 10000 Tk. in two 5 years term. He received 5% for the first term and 8% for the second term. What is the average rate of interest did he received?

ক
6.5%
খ
5.78%
গ
6.25%
ঘ
6.278%

ব্যাখ্যা

Question: Rakib invested 10000 Tk. in two 5 years term. He received 5% for the first term and 8% for the second term. What is the average rate of interest did he received?

Solution:
in first term, he received = 10000 × 5 × 5%
= 2500 Tk.
in second term, he received = 10000 × 5 × 8%
= 4000 Tk.
so,
total interest after 10 years, I = 6500
P = 10000
n = 10
r = ?

we know,
I = Pnr/100
r = 100I / Pn
= 650000/(10000 × 10)
= 6.5%

৪৪৭.

In January, the stock price went up by 50%. It then dropped by 20% in February, increased again by 25% in March, and declined by 10% in April. If Tk. 200 was invested initially and sold after April, calculate the net percentage change in price.

ক
28.5%
খ
30%
গ
41%
ঘ
25.5%
ঙ
None of these

ব্যাখ্যা

Question: In January, the stock price went up by 50%. It then dropped by 20% in February, increased again by 25% in March, and declined by 10% in April. If Tk. 200 was invested initially and sold after April, calculate the net percentage change in price.

Solution:
At the end of January,
The value of the stock is = Tk. 200 + 50% of (Tk. 200)
= Tk. 200 + Tk. 100 = Tk. 300.

At the end of February,
The value of the stock is = Tk. 300 - 20% of (Tk. 300)
= Tk. 300 - Tk. 60 = Tk. 240.

At the end of March,
The value of the stock is = Tk. 240 + 25% of (Tk. 240)
= Tk. 240 + Tk. 60 = Tk. 300.

At the end of April,
The value of the stock is = Tk. 300 - 10% of (Tk. 300)
= Tk. 300 - Tk. 30 = Tk. 270.

Now, the percentage change in price is,
= (Change in price/Original price) × 100%
= (270 - 200)/200 × 100%
= (70/200) × 100%
= 35%

৪৪৮.

In what time will Tk. 64000 amounts to Tk. 68921 at 5% per annum interest being compounded half yearly?

ক
1.5 years
খ
2 years
গ
2.5 years
ঘ
3 years
ঙ
3.5 years

ব্যাখ্যা

Question: In what time will Tk. 64000 amounts to Tk. 68921 at 5% per annum interest being compounded half yearly?

Solution:

∴ t = 1.5 years

৪৪৯.

A sum of Tk 7800 gives a simple interest of Tk. 702 in 2 years and 3 months. The rate of interest per annum is =?

ক
4%
খ
5%
গ
6%
ঘ
8%

ব্যাখ্যা

Question: A sum of Tk 7800 gives a simple interest of Tk. 702 in 2 years and 3 months. The rate of interest per annum is =?

Solution:
Time = 2 years 3 months
= 2 + (3/12)
= 2 + (1/4)
= (8 + 1)/4
= 9/4 years

Here,
I = 702
P = 7800
n = 9/4
r = ?

We know,
I = Pnr
⇒ r = I/pn
⇒ r = (702 × 4 × 100)/(7800 × 9)
∴ r = 4%

৪৫০.

The difference between the compound interest and the simple interest on a sum at 10% per annum for 2 years is Tk. 800. Find the principal.

ক
Tk. 60,000
খ
Tk. 68,000
গ
Tk. 80,000
ঘ
Tk. 88,000

ব্যাখ্যা

Question: The difference between the compound interest and the simple interest on a sum at 10% per annum for 2 years is Tk. 800. Find the principal.

Solution:
Given That,
r = 10%

We know,
Difference between C.I and S.I for 2 years
= p(r/100)²
= P(10/100)²

ATQ,
P(10/100)² = 800
⇒ P(1/10)² = 800
⇒ P(1/100) = 800
⇒ P = 800 × 100
∴ P = 80,000

Hence, Principal = Tk. 80,000

৪৫১.

A sum of money amounts to Tk. 920 in 3 years and to Tk. 1000 in 5 years. Find the rate percent per amount -

ক
ক) 3%
খ
খ) 4%
গ
গ) 5%
ঘ
ঘ) 6%

ব্যাখ্যা

After 5 years the sum = Tk. 1000
After 3 years the sum = Tk. 920

The interest of 2 years = Tk. (1000 - 920) = Tk. 80
The interest of 3 years, I = Tk. 80 x (3/2) = Tk. 120

The principle, P = Tk. (920 - 120) = Tk. 800
So, the rate = I/Pn = 120/(800 x 3) × 100% = 5%

৪৫২.

By investing in (40/5)% stock at Tk. 72, one earns Tk. 1800. The investment made is:

ক
Tk. 5640
খ
Tk. 6480
গ
Tk. 7200
ঘ
None of the above

ব্যাখ্যা

Question: By investing in (40/5)% stock at Tk. 72, one earns Tk. 1800. The investment made is:

Solution:
To earn Tk. 40/5, investment = Tk. 72
To earn Tk. 1, investment = Tk. 72 × (5/40)
To earn Tk. 1800, investment = Tk. {72 × (5/40) × 1800}
= Tk. 16200

৪৫৩.

An amount of Tk. 5000 becomes Tk. 9800 in 1 year. If the rate of interest is compound half yearly, what is the annual rate of interest?

ক
ক) 48%
খ
খ) 56%
গ
গ) 75.50%
ঘ
ঘ) 80%

ব্যাখ্যা

Question: An amount of Tk. 5000 becomes Tk. 9800 in 1 year. If the rate of interest is compound half yearly, what is the annual rate of interest?

Solution:
দেওয়া আছে,
মূলধন, P = 5000
চক্রবৃদ্ধি মূলধন, C = 9800

ধরি,
বাৎসরিক মুনাফার হার R

আমরা জানি,
C = P{1 + R/(2×100)}^2×1
9800 = 5000{1 + R/(200)}²
9800/5000 = {(200 + R)/200}²
49/25 = (200 + R)²/200²
(49/25) × 40000 = (200 + R)²
78400 = (200 + R)²
(200 + R)² =(280)²
R + 200 = 280
R = 80%

৪৫৪.

Kona deposited Tk. 505 into her savings account. If the interest rate of the account is 5% per year, how much interest will she have made after 4 years?

ক
ক) Tk. 101
খ
খ) Tk. 252.50
গ
গ) Tk. 606
ঘ
ঘ) Tk. 10,100

ব্যাখ্যা

We know, I = pnr
= 505 × 5/100 × 4
= 101

৪৫৫.

What is the amount of equal installment, if a sum of Tk.1,428 due 2 years hence has to be completely repaid in 2 equal annual installments starting next year?

ক
ক) Tk. 700
খ
খ) Tk. 800
গ
গ) Tk. 650
ঘ
ঘ) Cannot be determined

ব্যাখ্যা

সুদের হার না দেয়ার কারনে সুদাসলে বের করা সম্ভব নয়।
তাই EMI বা প্রদেয় কিস্তির পরিমাণ বের করা সম্ভব নয়।

৪৫৬.

How long (years) will it take a sum of money invested at 5% p.a. S. I. to increase its value by 40%?

ক
ক) 6 years
খ
খ) 8 years
গ
গ) 7 years
ঘ
ঘ) 5 years

ব্যাখ্যা

Let sum of money be Tk. x
S.I = 40% of x = 2x/5

Given rate =5%

Time =[100×(2x/5)×(1/5x)]
= 8 years

৪৫৭.

What is the total interest on Tk. 800 at 12.5% per annum for 9 months in taka?

ক
75
খ
10
গ
88
ঘ
22
ঙ
None of these

ব্যাখ্যা

Question: What is the total interest on Tk. 800 at 12.5% per annum for 9 months in taka?

Solution:
আসল, P = Tk. 800
সুদের হার, r = 12.5% = 0.125
বছর, n = 9 months = 9/12 year

সুদ = Pnr
= 800 × (9/12) × 0.125
= 75 Taka

৪৫৮.

A village's population is decreasing by 20% per year. If the population was 5000 two years ago, what is the current population?

ক
2000
খ
4200
গ
3200
ঘ
3600

ব্যাখ্যা

Question: A village's population is decreasing by 20% per year. If the population was 5000 two years ago, what is the current population?

Solution:
Given that,
The population of a village 2 years ago = 5000
Rate of growth = 20% p.a.
Time period = 2 years

Present population = P{(1 - (r/100)}ⁿ
= 5000 × {1 - (20/100)}²
= 5000 × {1 - (1/5)}²
= 5000 × (4/5)²
= 5000 × (16/25)
= 3200

৪৫৯.

A sum of money at simple interest amounts to TK. 5600 in 2 years and Tk. 6500 in 5 years at the rate of -

ক
ক) 3%
খ
খ) 4%
গ
গ) 5%
ঘ
ঘ) 6%

ব্যাখ্যা

Question: A sum of money at simple interest amounts to TK. 5600 in 2 years and Tk. 6500 in 5 years at the rate of -

Solution:
S.I. in 3 years = 6500 - 5600 = 900
Interest every year = 900/3 = 300
So, principal = 5600 - 2 × 300 = 5000

We know, I = pnr
Or, Interest rate, r = I/pn
= 600/(5000×2) × 100
= 6%

৪৬০.

If the interest of Tk. M at M% in 4 years is Tk. M, then M =?

ক
20
খ
25
গ
30
ঘ
32

ব্যাখ্যা

Question: If the interest of Tk. M at M% in 4 years is Tk. M, then M =?

Solution:
Here,
P = M
r = M%
I = M
n = 4

We know that,
I = Pnr
M = M × 4 × (M/100)
⇒ 1 = M/25
∴ M = 25

৪৬১.

5200 Taka is lent at compound interest of 10% per annum for 2 years. Find the amount after two years.

ক
Tk. 5280
খ
Tk. 6200
গ
Tk. 6292
ঘ
Tk. 7324
ঙ
None

ব্যাখ্যা

Question: 5200 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
= 5200 [1 + (10/100)]²
= 5200 × (110/100) × (110/100)
= 52 × 11 × 11
= 6292

Hence, The amount after two years is Tk. 6292

৪৬২.

At what rate percent of simple interest will a sum of money double itself in 20 years?

ক
6%
খ
8%
গ
5%
ঘ
4%

ব্যাখ্যা

Let sum be x
T = 20 years

Since the money doubles, simple interest = x
R = (100 × SI)/PT
= (100 × x)/(x × 20)
= 5%

৪৬৩.

What amount of money will amount to 750 in 6 years and to 800 in 8 years at simple interest?

ক
Tk. 550
খ
Tk. 700
গ
Tk. 650
ঘ
Tk. 600

ব্যাখ্যা

Question: What amount of money will amount to 750 in 6 years and to 800 in 8 years at simple interest?

Solution:
In two years the interest becomes = 800 - 750 = 50Tk.
∴ Interest in 1 year = 25
∴ Interest in 6 year = 25 × 6 = 150

Principal = Amount - SI
= 750 - 150 = Tk. 600

৪৬৪.

The simple interest on a sum of money in 5 years at 12% per annum is Tk. 400 less than the simple interest accrued on the same sum in 7 years at 10% per annum. Find the sum.

ক
Tk. 3800
খ
Tk. 4200
গ
Tk. 4000
ঘ
Tk. 5000

ব্যাখ্যা

Question: The simple interest on a sum of money in 5 years at 12% per annum is Tk. 400 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 = 400
⇒ 0.1 P = 400
⇒ P = 4000
Thus, the required sum is Tk. 4000

৪৬৫.

A sum of money lent out at simple interest amounts to Tk. 720 after 2 years and Tk. 1020 after a further period of 5 years. Find the principal?

ক
Tk. 6000
খ
Tk. 620
গ
Tk. 600
ঘ
Tk. 120

ব্যাখ্যা

Question: A sum of money lent out at simple interest amounts to Tk. 720 after 2 years and Tk. 1020 after a further period of 5 years. Find the principal?

Solution:
According to the question,
Principal + Simple interest for 2 year = Tk. 720 ------------- (1)
Principal + Simple interest for 7 year = Tk. 1020 ------------ (2)

Subtracting equation (1) from (2)
Principal + Simple interest for 7 year = Tk. 1020
Principal + Simple interest for 2 year = Tk. 720
∴ Simple interest for 5 years = Tk. 300
⇒ Simple interest for 1 years = Tk. 300/5
⇒ Simple interest for 1 years = Tk. 60
⇒ Simple interest for 2 years = Tk. (60 × 2)
∴ Simple interest for 2 years = = Tk. 120

∴ Principal amount = (Amount after 2 years - 2 years Simple interest)
⇒ Principal amount = Tk. (720 - 120)
∴ Principal amount = Tk. 600

৪৬৬.

If interest is compounded every six months, how much interest will Tk. 4000 earn at a 10% annual rate in a year?

ক
Tk. 205
খ
Tk. 820
গ
Tk. 810
ঘ
Tk. 410

ব্যাখ্যা

Question: If interest is compounded every six months, how much interest will Tk. 4000 earn at a 10% annual rate in a year?

Solution:
Here,
Interest rate, r = 10% per year
= (10/2)% per 6 months
= 5% per 6 months
P = Tk. 4000
n = 2

∴ C = P(1 + r)ⁿ
= 4000 {1 + (5/100)}²
= 4000 × (105/100) × (105/100)
= 4000 × (21/20) × (21/20)
= 4410

∴ Interest is = Tk. 4410 - 4000
= Tk. 410

৪৬৭.

In what time will the simple interest of Tk. 400 at 10% per annum be the same as the simple interest Tk. 1000 for 4 year at 4% per annum?

ক
3 years
খ
4 years
গ
5 years
ঘ
6 years
ঙ
None of the above

ব্যাখ্যা

Simple interest I = pnr/100
A/Q, (400 × 100 × n)/100 = (1000 × 4 × 4)/100
Or, 4000n = 16000
Or, n = 4

৪৬৮.

Rahim invested 20,000 Tk. in two 4 years term. He received 6% for the first term and 9% for the second term. What is the average rate of interest did he receive?

ক
6.5%
খ
7.5%
গ
5%
ঘ
6%

ব্যাখ্যা

Question: Rahim invested 20,000 Tk. in two 4 years term. He received 6% for the first term and 9% for the second term. What is the average rate of interest did he receive?

Solution:
In first term, he received = 20,000 × 4 × 6%
= 4,800 Tk.
In second term, he received = 20,000 × 4 × 9%
= 7,200 Tk.

So, total interest after 8 years, I = 4,800 + 7,200 = 12,000
P = 20,000
n = 8
r = ?

We know,
I = Pnr/100
∴ r = (100 × I)/Pn
= (100 × 12,000)/(20,000 × 8)
= 7.5%

∴ The average rate of interest Rahim received = 7.5%

৪৬৯.

Compound interest on a certain sum for 2 years at 10% per annum is Tk. 630. What would be the simple interest at the same rate and for the same time?

ক
Tk. 1500
খ
Tk. 3000
গ
Tk. 900
ঘ
Tk. 600

ব্যাখ্যা

Question: Compound interest on a certain sum for 2 years at 10% per annum is Tk. 630. What would be the simple interest at the same rate and for the same time?

Solution:
Let, Principle = P
Compound Principle, C = P(1 + r)n
= P(1 + 10/100)2

ATQ,
C - P = 630
⇒ P(1 + 10/100)² - P = 630
⇒ P{(11/10)² - 1} = 630
⇒ P{(121/100) - 1} = 630
⇒ P(121- 100)/100 = 630
⇒ P(21/100) = 630
⇒ P = (630 × 100)/21
∴ P = 3000

Again,
I = Pnr
= 3000 × 2 × (10/100)
= 600

∴ The simple interest would be Tk. 600.

৪৭০.

On a certain sum of money the compound interest Tk. 318 is earned in 2 years. If the rate of interest is 12%, what is the principal amount?

ক
Tk. 1250
খ
Tk. 1300
গ
Tk. 1200
ঘ
Tk. 1150

ব্যাখ্যা

Question: On a certain sum of money the compound interest Tk. 318 is earned in 2 years. If the rate of interest is 12%, what is the principal amount?

Solution:
C = P(1 + r)ⁿ
Compound Interest = C - P
∴ P(1 + 12/100)² - P = 318
⇒ P{(112/100)² - 1} = 318
⇒ P{(1.12 × 1.12) - 1} = 318
⇒ P(1.2544 - 1) = 318
⇒ P(0.2544) = 318
⇒ P = 318/0.2544
∴ P = 1250

৪৭১.

Simple interest on a certain sum at the rate of 4.5% p.a for 4 years and 6 years differs by BDT 216. The sum is-

ক
ক) BDT 2100
খ
খ) BDT 2400
গ
গ) BDT 1800
ঘ
ঘ) None of these

ব্যাখ্যা

Question: Simple interest on a certain sum at the rate of 4.5% p.a for 4 years and 6 years differs by BDT 216. The sum is-

Solution:
Let the sum be Tk. P
Then,
216 = {(P × 4.5 × 6)/100} - {(P × 4.5 × 4)/100}
216 = (27P - 18P)/100
21600 = 9P
P = 21600/9
P = 2400

৪৭২.

A sum of 10,000 Taka is invested at 8% per annum. If the interest is compounded quarterly, the amount after 1 year will be:

ক
10,800 Taka
খ
10,833 Taka
গ
10,815 Taka
ঘ
10,824 Taka

ব্যাখ্যা

Question: A sum of 10,000 Taka is invested at 8% per annum. If the interest is compounded quarterly, the amount after 1 year will be:

Solution:
The annual rate is 8%.
Since interest is compounded quarterly, the quarterly rate is:
8%/4 = 2% per quarter

Time period is 1 year, meaning there are 4 quarters.

We apply 2% interest every quarter.

First Quarter:
New Amount=10,000 + (2% of 10,000) = 10,000+200= 10,200

Second Quarter:
New Amount=10,200 + (2% of 10,200) =10,200+204= 10,404

Third Quarter:
New Amount=10,404 + (2% of 10,404) =10,404+208.08= 10,612.08

Fourth Quarter:
New Amount=10,612.08 + (2% of 10,612.08) =10,612.08+212.24= 10,824.32

So, The final amount after 1 year is 10,824 Taka.

৪৭৩.

A certain sum of money doubles in 20 years at simple interest. What is the annual rate of interest?

ক
5%
খ
8%
গ
10%
ঘ
12%
ঙ
None

ব্যাখ্যা

Question: A certain sum of money doubles in 20 years at simple interest. What is the annual rate of interest?

Solution:
Let,
sum = P,
then simple interest = P
and Time, T = 20 years

∴ Required rate = (100 × SI)/(P × T)
= (100 × P)/(P × 20)
= 5% per annum

৪৭৪.

A sum of Tk. 12000 deposited at compound interest become double after 5 years. After 20 years it will become ?

ক
ক) Tk. 96,000
খ
খ) Tk. 1,20,000
গ
গ) Tk. 1,24,000
ঘ
ঘ) Tk. 1,92,000

ব্যাখ্যা

12000 × (1 + R/100)⁵ = 24000
⇒ (1 + R/100)⁵ = 2
⇒ {(1 + R/100)⁵}⁴ = 2⁴ = 16
⇒ (1 + R/100)²⁰ = 16
⇒ P(1 + R/100)²⁰ = P16
⇒ 12000(1 + R/100)²⁰ = 16 × 12000 = Tk. 1,92,000

৪৭৫.

A sum of money becomes 7/ 5 of itself in 4 years at a certain rate of simple interest. What is the rate of interest per annum?

ক
10%
খ
12%
গ
14%
ঘ
18%
ঙ
7%

ব্যাখ্যা

Let the sum be x
Amount after 4 years = 7x /5
SI for 4 years = 7x/ 5 − x = 2x/5
R = (100 × SI)/ PT
= (100 × 2 x /5)/( x × 4)
= 10

Alternative:
The sum makes 2 /5 of itself in 4 years.
That is , 40 % in 4 years. That is 10% each year.
Therefore, rate of interest per annum is 10%.

৪৭৬.

Find the compound interest, if Tk. 1000 was invested for 1.5 years at 20% p.a. compounded half yearly.

ক
Tk. 300
খ
Tk. 1300
গ
Tk. 331
ঘ
Tk. 1331

ব্যাখ্যা

Question: Find the compound interest, if Tk. 1000 was invested for 1.5 years at 20% p.a. compounded half yearly.

Solution:
As it is said that the interest is compounded half yearly. So, the rate of interest will be halved and time will be doubled.
CI = P [1 + (R/100)]ⁿ - P
CI = 1000[1 +(10/100)]³ - 1000
CI = 1000 × 1.1 × 1.1 × 1.1 - 1000
CI = 1331 - 1000
CI = 331

৪৭৭.

A man buys tk. 20 shares paying 9% dividend. The man wants to have an interest of 12% on his money. The market value of each share is:

ক
ক) Tk.10
খ
খ) Tk.15
গ
গ) Tk.12
ঘ
ঘ) Tk.18

ব্যাখ্যা

Question: A man buys tk. 20 shares paying 9% dividend. The man wants to have an interest of 12% on his money. The market value of each share is:

Solution:
Dividend on Tk.20 = Tk. {(9/100) × 20}
= Tk. 9/5

Tk.12 is an income on Tk.100
∴ Tk. 9/5 is an income on = Tk.(100/12) × (9/5)
= Tk.15

৪৭৮.

S.I. on Tk. 1500 at 7% per annum for a certain time is Tk. 210. Find the time.

ক
3 years
খ
1.5 years
গ
2 years
ঘ
2.8 years

ব্যাখ্যা

Question: S.I. on Tk. 1500 at 7% per annum for a certain time is Tk. 210. Find the time.

Solution:
P = 1500
r = 7%
I = 210
n = ?

n = I/(Pr)
= (210 × 100)/(1500 × 7)
= 2 years

৪৭৯.

A sum of Tk. 10,000 amounts to Tk. 12,000 in 4 years at the rate of simple interest. What is the rate of interest?

ক
ক) 4%
খ
খ) 5%
গ
গ) 6%
ঘ
ঘ) 7%

ব্যাখ্যা

Question: A sum of Tk. 10,000 amounts to Tk. 12,000 in 4 years at the rate of simple interest. What is the rate of interest?

Solution:
সুদ = ১২০০০ - ১০০০০ টাকা
= ২০০০ টাকা

ধরি, সুদের হার r%

I = pnr
⇒ 2000 = 10000 × 4 × r/100
⇒ r = 5

সুদের হার ৫%

৪৮০.

A sum of money triples itself in 6 years at compound interest. In how many years will it amount to 27 times itself at the same rate of interest?

ক
12 years
খ
18 years
গ
9 years
ঘ
21 years

ব্যাখ্যা

Question: A sum of money triples itself in 6 years at compound interest. In how many years will it amount to 27 times itself at the same rate of interest?

Solution:
let,
the sum = P

ATQ,
3P = P(1 + r)⁶
⇒ (1 + r)⁶ = 3

Again,
let, sum will 27 times in n years

Then,
27P = P(1 + r)ⁿ
⇒ 27 = (1 + r)ⁿ
⇒ 3³ = (1 + r)ⁿ
⇒ {(1 + r)⁶}³ = (1 + r)ⁿ
⇒ (1 + r)¹⁸ = (1 + r)ⁿ
∴ n = 18

৪৮১.

The population of a village decreases at the rate of 25% per annum. If its population 2 years ago was 24000, the present population is =?

ক
13000
খ
13500
গ
12500
ঘ
14500

ব্যাখ্যা

Question: The population of a village decreases at the rate of 25% per annum. If its population 2 years ago was 24000, the present population is =?

Solution:
Given that,
The population of a village 2 years ago = 24000
Rate of growth = 25% p.a.
Time period = 2 years

Present population = P{(1 - (r/100)}ⁿ
= 24000 × {1 - (25/100)}²
= 24000 × {1 - (1/4)}²
= 24000 × (3/4)²
= 24000 × (9/16)
= 13500

৪৮২.

Find the compound interest on Tk. 8500 at 4 % per annum for 2 years, compounded annually.

ক
Tk 592.4
খ
Tk 598.8
গ
Tk 693.6
ঘ
Tk 685.3

ব্যাখ্যা

Question: Find the compound interest on Tk. 8500 at 4 % per annum for 2 years, compounded annually.

Solution:
Principal = Tk. 8500, Rate = 4 % per annum, Time = 2 years
Amount = 8500 {1 + (4/100)}²
= Tk. 9193.6

Compound Interest = Total amount - Principal
= 9193.6 - 8500
= 693.6

৪৮৩.

At what rate of compound interest per annum will a sum of Tk. 2500 become Tk. 3600 in 2 years?

ক
15%
খ
20%
গ
30%
ঘ
12%

ব্যাখ্যা

প্রশ্ন: At what rate of compound interest per annum will a sum of Tk. 2500 become Tk. 3600 in 2 years?

সমাধান:
দেওয়া আছে,
মূলধন, P = 2500 টাকা
চক্রবৃদ্ধি আসল, C = 3600 টাকা
সময়, n = 2 বছর
মুনাফার হার = r ?

আমরা জানি,
চক্রবৃদ্ধি আসল, C = P(1 + r/100)ⁿ
⇒ 3600 = 2500(1 + r/100)²
⇒ (1 + r/100)² = 3600/2500
⇒ (1 + r/100)² = 36/25
⇒ 1 + r/100 = 6/5
⇒ r/100 = (6/5) - 1
⇒ r/100 = 1/5
⇒ r = (1 × 100) / 5
⇒ r = 20

∴ বার্ষিক চক্রবৃদ্ধি সুদের হার = 20%

৪৮৪.

A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay. Tk. 5,400 interest only for the period, The principal amount borrowed by him was:

ক
ক) Tk. 20,000
খ
খ) Tk. 15,000
গ
গ) Tk. 10,000
ঘ
ঘ) Tk. 5,000

ব্যাখ্যা

Question: A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay. Tk. 5,400 interest only for the period, The principal amount borrowed by him was:

Solution:
Given,
Rate of interest, r = 12%= 12/100
Time, n = 3 years
Interest, I = Tk. 5400

Principal, P =?

We know,
I = Pnr
Or, 5400 = P × 3 × (12/100)
Or, P = (5400 × 100)/(3 × 12)
∴ P = 15000

৪৮৫.

Krishna invests Tk. 500 in the A Bank of Bangladesh at a simple interest rate of 8%. How much will be in his account after 5 years?

ক
ক) Tk. 550
খ
খ) Tk. 540
গ
গ) Tk. 700
ঘ
ঘ) Tk. 800

ব্যাখ্যা

প্রশ্ন: Krishna invests Tk. 500 in the A Bank of Bangladesh at a simple interest rate of 8%. How much will be in his account after 5 years?

সমাধান:
Let,
P = Tk. 500
r = 8% = 8/100
n = 5 years

∴ I = Pnr
= 500 × 5 × (8/100)
= 200

∴ total amount after 5 years will be = (500 + 200)
= Tk. 700

৪৮৬.

Compute the annual interest from a deposit of Tk. 20,000 under an 8% simple interest scheme.

ক
Tk. 1850
খ
Tk. 2100
গ
Tk. 2200
ঘ
Tk. 1600

ব্যাখ্যা

Question: Compute the annual interest from a deposit of Tk. 20,000 under an 8% simple interest scheme.

Solution:
Here,
Principal, P = Tk. 20000
Rate, r = 8%
Time, n = 1 year (since "annual" interest means for one year)

We know,
I = Prn
= 20000 × 8% × 1
= 20000 × (8/100)
= 1600

Thus, the annual interest accrued is Tk. 1600.

৪৮৭.

Samia owns a hairdressing salon. She borrows Tk. 5000 from a bank to improvements to her beauty salon. She is charged 5% per year compound interest. She pays the money back after 2 years. Calculate the total amount Samia must pay to the bank.

ক
ক) Tk. 5820.5
খ
খ) Tk. 5650.5
গ
গ) Tk. 5250.5
ঘ
ঘ) Tk. 5512.5

ব্যাখ্যা

Question: Samia owns a hairdressing salon. She borrows Tk. 5000 from a bank to improvements to her beauty salon. She is charged 5% per year compound interest. She pays the money back after 2 years. Calculate the total amount Samia must pay to the bank.

Solution:
এখানে,
P = 5000 টাকা
r = 5%, = 5/100
n = 2 বছর

চক্রবৃদ্ধি মলধন C = P (1 + r)ⁿ
= 5000(1 + 5/100)²
= 5000 × (105/100)²
= 5000 × 1.1025
= 5512.5

৪৮৮.

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 -

ক
Tk 10,000
খ
Tk 7,000
গ
Tk 9,000
ঘ
Tk 17,000

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 the 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

৪৮৯.

At the rate of 8% simple interest, a sum of Tk. 2800 will earn how much interest in 2 years 6 months?

ক
ক) Tk. 580
খ
খ) Tk. 575
গ
গ) Tk. 560
ঘ
ঘ) Tk. 460

ব্যাখ্যা

Question: At the rate of 8% simple interest, a sum of Tk. 2800 will earn how much interest in 2 years 6 months?

Solution:
Given,
Principal, P = 2800 Tk.
Rate of interest, r = 8% = 8/100 = 2/25.
Time, n = 2 years 6 months
⇒ n = 2 + (6/12) years
∴ n = 5/2 years.

We know,
I = Pnr
= 2800 × (5/2) × (2/25)
= 560 Tk.
Simple Interest Tk. 560.

৪৯০.

Ankita deposited Tk. 750 into her savings account. If the interest rate of the account is 4% per year, how much interest will she have made after 5 years?

ক
ক) Tk. 131
খ
খ) Tk. 142
গ
গ) Tk. 150
ঘ
ঘ) Tk. 168

ব্যাখ্যা

We know, I = pnr
= 750 × 5/100 × 4
= 150

৪৯১.

There is 45% increase in an amount in 4 years 6 months at simple interest. What will be the compound interest of Tk. 10000 after 4 years at the same rate?

ক
Tk. 4000
খ
Tk. 4641
গ
Tk. 14641
ঘ
Tk. 14000

ব্যাখ্যা

Question: There is 45% increase in an amount in 4 years 6 months at simple interest. What will be the compound interest of Tk. 10000 after 4 years at the same rate?

Solution:
Let,
P = Tk. 100.
∴ Simple interest, I = Tk. 45
n = 4 years 6 months = 4.5 years
Rate = r

We know that,
I = Pnr
∴ r = I/(Pn)
= (45 × 100)/(100 × 4.5) %
= 10%

Now,
P = Tk. 10000
n = 4 years
r = 10%

C = P(1 + r)ⁿ
= 10000 × (1.1)⁴
= 10000 × 1.1 × 1.1 × 1.1 × 1.1
= 14641

∴ The compound interest = Tk. (14641 - 10000) = Tk. 4641

৪৯২.

A man invests Tk. 8100 partly in 14% stock at 294 and partly in 12% stock at 288. If his income from both is the same, find his investment in the 14% stock.

ক
Tk. 3345
খ
Tk. 4780
গ
Tk. 4000
ঘ
Tk. 3780

ব্যাখ্যা

Question: A man invests Tk. 8100 partly in 14% stock at 294 and partly in 12% stock at 288. If his income from both is the same, find his investment in the 14% stock.

Solution:
Let he invests x at 14% stock.
x Investment at 12% stock = 8100 - x

As income is same.
x × (14/100) × (1/294) = (8100 - x) × (12/100) × (1/288)
⇒ x/2100 = (8100 - x)/2400
⇒ x = {(8100 - x)/2400} × 2100
⇒ 24x = 170100 - 21x
⇒ 45x = 170100
∴ x = Tk3780

৪৯৩.

What is the compound amount of Tk. 16000 for 2 years at a rate of interest of 5% per annum?

ক
Tk. 11640
খ
Tk. 27640
গ
Tk. 17640
ঘ
Tk. 16640

ব্যাখ্যা

Question: What is the compound amount of Tk. 16000 for 2 years at a rate of interest of 5% per annum?

Solution:
Given,
Principal, P = 16000
Rate, r = 5% = 5/100 = 1/20
Time, n = 2 years

We know,
A = P(1 + r)ⁿ
= 16000 × (1 + 1/20)²
= 16000 × (21/20)²
= (16000 × 21 × 21)/(20 × 20)
= (16000 × 441)/400
= 40 × 441
= 17640

∴ The compound amount is Tk. 17640.

৪৯৪.

What sum of money will amount to Tk. 1500 in 5 years and to Tk. 1620 in 7 years at simple interest?

ক
1100 Tk.
খ
1200 Tk.
গ
1180 Tk.
ঘ
1150 Tk.

ব্যাখ্যা

Question: What sum of money will amount to Tk. 1500 in 5 years and to Tk. 1620 in 7 years at simple interest?

Solution:
in two years the interest becomes = 1620 - 1500 = 120Tk.
in 5 years, interest = (120/2)/5 =300 Tk.

so , the principle amount is = 1500 - 300 = 1200 Tk.

৪৯৫.

Find the income of 8% stock of Tk.1200 purchased at Tk.120 -

ক
ক) Tk. 88
খ
খ) Tk. 85
গ
গ) Tk.105
ঘ
ঘ) Tk. 110
ঙ
ঙ) Tk. 96

ব্যাখ্যা

Face Value = Tk.1200
Market Value = Tk.120
Dividend (income) = (1200 × 8)/100
= Tk.96

৪৯৬.

At an annual interest rate of 10%, the difference between compound interest (CI) and simple interest (SI) on a sum of money for 2 years is 250 Taka. What is the principal amount?

ক
20000 Taka
খ
15000 Taka
গ
25000 Taka
ঘ
10000 Taka

ব্যাখ্যা

Question: At an annual interest rate of 10%, the difference between compound interest (CI) and simple interest (SI) on a sum of money for 2 years is 250 Taka. What is the principal amount?

Solution:
Let the principal = P Taka
Rate of interest, r = 10%
Time, n = 2 years

We know,
Simple Interest (SI) = P×r×n/100
= (P × 10 × 2) /100
= P/5

Again,
Compound Interest (CI) = P{1 + ( r/100)}ⁿ−P
= P {1+ (10/100)}²−P
= P {1 + (1/10)}² - P
= P (11/10)²− P
= ( 121P/100 ) − P
= (121P - 100P) /100
= 21P/100

According to the question,
Compound Interest – Simple Interest = 250
So,
( 21P/100 ) − ( P/5 ) =250
⇒ (21P − 20P) /100 = 250
⇒ P/100 = 250
⇒ P = 250 × 100 = 25000

Therefore, the principal = 25000 Taka.

৪৯৭.

A man invested Tk. 18000 in Tk. 100 shares of a company at 25% premium. If the company declares 6% dividend at the end of the year, then how much does he get?

ক
Tk. 812
খ
Tk. 1022
গ
Tk. 948
ঘ
Tk. 864

ব্যাখ্যা

Question: A man invested Tk. 18000 in Tk. 100 shares of a company at 25% premium. If the company declares 6% dividend at the end of the year, then how much does he get?

Solution:
Number of shares = 18000/125
= 144
Face value = Tk. (100 × 144)
= Tk. 14400
∴ Annual income = Tk. (6/100) × 14400
= Tk. 864

৪৯৮.

A sum of money doubles itself in 10 years at simple interest. What is the annual interest rate?

ক
10%
খ
15%
গ
2.5%
ঘ
5%

ব্যাখ্যা

Question: A sum of money doubles itself in 10 years at simple interest. What is the annual interest rate?

Solution:
Let,
Principal amount = P
Sum of amount = 2P
∴ Interest, I = 2P - P = P
Time, n = 10 years
Rate of interest = r

We know,
I = Pnr
∴ r = I/Pn
= P/(P × 10)
= 1/10 × 100%
= 10%

৪৯৯.

Tk. 6100 was partly invested in Scheme A at 10% p.a. compound interest for 2 years and partly in Scheme B at 10% p.a. simple interest for 4 years. Both the schemes pay equal interests. How much was invested in Scheme B?

ক
Tk. 4500
খ
Tk. 2100
গ
Tk. 5000
ঘ
Tk. 4000

ব্যাখ্যা

Question: Tk. 6100 was partly invested in Scheme A at 10% p.a. compound interest for 2 years and partly in Scheme B at 10% p.a. simple interest for 4 years. Both the schemes pay equal interests. How much was invested in Scheme A?

Solution:
Total sum = Tk. 6100
In Scheme A, Compound interest
Principal = P
R = 10% per annum for 2 years

In Scheme B, Simple interest
Principal = 6100 - P
R = 10% per annum for 4 years

Here,
Compound interest = Simple interest
⇒ P[{1 + (R/100)}ⁿ - 1] = (PRN)/100
⇒ P[{1 + 10/100}² - 1] = [(6100 - P) × 4 × 10]/100
⇒ P× (21/100) = [(6100 - P) × 4 × 10]/100
⇒ 21P = 6100 × 40 - 40P
⇒ 61P = 6100 × 40
∴ P = 4000

∴ The amount invested in Scheme B is Tk. (6100 - 4000) = Tk. 2100

৫০০.

What is the total interest on Tk 800 at 12.5% per annum for 9 months (in taka)?

ক
75
খ
110
গ
88
ঘ
22
ঙ
None of these

ব্যাখ্যা

Question: What is the total interest on Tk 800 at 12.5% per annum for 9 months (in taka)?

Solution:
আসল, P = Tk. 800
সুদের হার, r = 12.5% = 0.125
বছর, n = 9 months = 9/12 year

সুদ = Pnr
= 800 × (9/12) × 0.125
= 75 Taka