লগ ইননিবন্ধন
পরীক্ষা আর্কাইভ

ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

পরীক্ষাব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্সতারিখতারিখ অনির্ধারিতসময়45 minutes২৭ বৈধ · ১ অসম্পূর্ণ
মোট প্রশ্ন২৮
সিলেবাস
Math - 09 - Simple & Compound Interest, Stocks & Shares
প্রশ্ন দেখুনঅনুশীলন
ঘনত্ব
উত্তর
উত্তরিতবর্তমানপুনরায় দেখুনঅসম্পূর্ণ

ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স · তারিখ অনির্ধারিত · ২৮ প্রশ্ন

১.
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.

২.
The sum invested in scheme B is thrice the sum invested in scheme A. The investment in scheme A is made for 4 years at 8% p.a. simple interest and in scheme B for 2 years at 13% p.a. simple interest. The total interest earned from both the schemes is Tk. 1320. How much amount was invested in scheme A?
  1. ক
    ক) Tk. 1200
  2. খ
    খ) Tk. 1100
  3. গ
    গ) Tk. 960
  4. ঘ
    ঘ) Tk. 1500
ব্যাখ্যা

Let the amount invested in scheme A be Tk. x and that in B be Tk. 3x.
Then,
Then,
{(x × 4 × 8)/100 + (3x × 2 × 13)/100} = 1320
⇒ 32x/100 + 78x/100 = 1320
⇒ 110x/100 = 1320
⇒ x = (1320 × 100)/110
⇒ x = Tk. 1200

Hence, Tk. 1200 was invested in scheme A.

৩.
Soma borrowed Tk. 50,000 for 3 years at the rate of 3.5% per annum. Find the interest accumulated at the end of 3 years.
  1. ক
    ক) Tk. 4750
  2. খ
    খ) Tk. 5000
  3. গ
    গ) Tk. 5250
  4. ঘ
    ঘ) Tk. 5580
ব্যাখ্যা

Given that,
P = Rs 50,000
R = 3.5%
T = 3 years

S.I.
= (P × R × T)/100
= (50,000 × 3.5 × 3)/100
= Tk. 5250.

৪.
A principal amount of Tk. 10,000 is taken at 15% interest rate p.a. for two years. Calculate the SI on this sum and the final payable amount.
  1. ক
    ক) Tk. 12000
  2. খ
    খ) Tk. 12500
  3. গ
    গ) Tk. 12750
  4. ঘ
    ঘ) Tk. 13000
ব্যাখ্যা

Interest charged on Tk 10,000 is,
(15/100) × 10000 = Tk. 1500

Interest for two years =
Tk. 1500 × 2 = Tk. 3000

The amount payable after two years = principal + interest
= Tk. 10000 + Tk. 3000 = Tk. 13000

৫.
A person invested in some account at the rate of 12% simple interest and a certain amount at rate of 10% simple interest. He received yearly interest of Tk. 130. But if he had interchanged the amounts invested, he would have received Tk. 4 more as interest. How much did he invest at 12% simple interest?
  1. ক
    ক) Tk. 400
  2. খ
    খ) Tk. 500
  3. গ
    গ) Tk. 700
  4. ঘ
    ঘ) Tk. 800
ব্যাখ্যা

Let,
The amount invested at 12% be Tk. x and that invested at 10% be Tk. y
Then, 12% x + 10% of y = 130
⇒ 12x + 10y = 13000
⇒ 6x + 5y = 6500 .............(i)

And, 10% x + 12% of y = 134
⇒ 10x + 12y = 13400
⇒ 5x + 6y = 6700 .......(ii)

Adding (i) and (ii) we get,
11(x + y) = 13200
⇒ x + y = 1200 ..........(iii)

Subtracting (i) from (ii) we get,
x + y = 200 .........(iv)

Adding (iii) and (iv) we get,
2y = 1400
⇒ y = 700

∴ x = 1200 - 700 = 500

So,
The amount invested at 12% is TK 500
And the amount invested at 10% is TK 700.

৬.
A man buys a TV priced at Tk. 16000. He pays Tk. 4000 at once and the rest after 15 months on which he charges a simple interest at the rate of 12% per year. The total amount he pays for TV is -
  1. ক
    ক) Tk. 18200
  2. খ
    খ) Tk. 17800
  3. গ
    গ) Tk. 17200
  4. ঘ
    ঘ) Tk. 16800
ব্যাখ্যা

Total price of TV = Tk. 16000
Initial payment = Tk. 4000
Remaining amount = Tk. 12000
Simple interest in 15 months for Tk. 12000

S.I. = (P × R × T)/100
= ( 12000 × 12 × 15)/(100 × 12)
= Tk. 1800

⇒ With S.I. total amount to be paid for principal amount Tk. 12000
= Tk. (12000 + 1800)
= Tk. 13800

Therefore,
total amount he pays for the TV is
= 4000 + 13800
= Tk. 17800

৭.
Rohit lends his 40800 Tk in two parts at simple interest. He lends one part for a period of 8 years at a rate of 6.25%. The other part he lends for 5 years at a rate of 7%. Both the parts earn him the same interest. Find the value of the smaller part of money.
  1. ক
    ক) Tk. 13000
  2. খ
    খ) Tk. 16800
  3. গ
    গ) Tk. 19200
  4. ঘ
    ঘ) Tk. 20100
ব্যাখ্যা

Two parts are = A and (40800 - A)
Time period and Simple interest are same for both

Simple Interest = (P × R × T)/100

∴ (A × 6.25 × 8)/100 = {(40800 - A) × 7 × 5}/100
∴ 50A = 35 × 40800 - 35A
∴ 85A = 35 × 40800
∴ A = 8400

Smaller amount is Tk. 16800
By direct observation, we can say that 16800 is smaller - as it is smaller than half of 40800.

৮.
If a sum doubles in 6 years, how much will it be in 8 years?
  1. ক
    ক) 1(1/2) years
  2. খ
    খ) 1(1/3) years
  3. গ
    গ) 1(1/4) years
  4. ঘ
    ঘ) 1(3/4) years
অনির্ধারিত
ব্যাখ্যা

Let Sum = Tk. x. Then, S.I. = Tk. x, Time = 16 years
Rate = {(100 × x)/(x × 16)}%
= (25/4)%
= 6(1/4)%

Now,
Sum =Tk. x,
Time = 8 years
Rate = 6(1/4)%

∴ S.I. = Tk. {(x × 25 × 8)/(100 × 4)}
= Tk. x/2
So, amount = Tk. (x + x/2)
= Tk. 3x/2
= 1(1/2) times

প্রশ্নে ৬ - এর স্থলে ১৬ হলে উত্তর ঠিক ছিলো।
৯.
A certain amount becomes Tk. 3000 at a simple interest of 12%. Keeping the time period the same, if the rate of simple interest is increased by 3%, the amount will become 300 Tk/- more than in the previous setting. What is the amount? Also find the time period.
  1. ক
    ক) Tk. 1500 and 7 years
  2. খ
    খ) Tk. 1800 and 5.5 years
  3. গ
    গ) Tk. 1900 and 8.25 years
  4. ঘ
    ঘ) Tk. 2000 and 20 years
ব্যাখ্যা

Let Simple Interest be S
Original sum 'P' and Time 'T' remains the same
Also, 3% increase in rate of interested means, New rate = 15%
Increase of 300 Rs/- in the final amount means, New amount = Tk. 3300/-

So, Amount 2 - Amount 1 = (P + S1) - (P + S2) = S1 - S2
∴ 3300 - 3000 = S1 - S2
∴ S1 - S2 = 300

∴ {(P × R × T)/100} - {(P × 12 × T)/100 = 300
3PT/100 = 300
PT = 10000
For R = 15%,

Simple interest = (P × 15 × T)/100
= (10000 × 15)/100
= Tk. 1500

Original sum = Amount - Interest = 3300 - 1500 = Tk. 1800 (Principle amount)

Also, PT = 10000
T = 10000/1800
= 5.55 years.

১০.
A computer is available for Tk. 39000 cash or Tk. 17000 as cash down payment followed by five monthly instalments of Tk. 4800 each. What is the rate of interest under the instalment plan?
  1. ক
    ক) 35.71% p.a.
  2. খ
    খ) 36.71% p.a.
  3. গ
    গ) 37.71% p.a.
  4. ঘ
    ঘ) 38.71% p.a.
ব্যাখ্যা

Total cost of the computer = Tk. 39000
Down payment = Tk. 17000
Balance = Tk. (39000 - 17000) = Tk. 22000.
Let the rate of interest be R% p.a.
Amount of Tk. 22000 for 5 months
= {22000 + 22000 × (5/12) × R/100}
= {22000 + (275R/3)}

The customer pays the shopkeeper Tk. 4800 after 1 month,
Tk. 4800 after 2 months, ...... and Tk. 4800 after 5 months.

Thus, the shopkeeper keeps Tk. 4800 for 4 months, Tk. 4800 for 3 months, Tk. 4800 for 2 months, Tk. 4800 for 1 months and Tk. 4800 at the end.

∴ sum of the amounts of these installments
= (Tk. 4800 + S.I. on Tk. 4800 for 4 months) + (Tk. 4800 + S.I. on Tk. 4800 for 3 months) + ...... + (Tk. 4800 + S.I. on Tk. 4800 for 1 month) + Tk. 4800
= Tk. (4800 × 5) + S.I. on Tk. 4800 for (4 + 3 + 2 + 1) months
= Tk. 24000 + S.I. on Tk. 4800 for 10 months
= 24000 × 4800 × R × (10/12) × (1/100)
= (24000 + 40 R)

∴ {22000 + (275R/3)} = (24000 + 40 R)
⇒ 155R/3 = 2000
⇒ R = (2000 × 3)/155
= 38.71

১১.
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 -
  1. ক
    ক) Tk. 1620
  2. খ
    খ) Tk. 1640
  3. গ
    গ) Tk. 1680
  4. 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.

১২.
At the end of 3 years, the difference between the compound interest and simple interest comes to be Tk. 320. The rate of interest is 25%. Find the principal amount.
  1. ক
    ক) Tk. 1525.50
  2. খ
    খ) Tk. 1545.78
  3. গ
    গ) Tk. 1550
  4. ঘ
    ঘ) Tk. 1575.38
ব্যাখ্যা

Principle = P
Compound Interest = Total amount - Principle
P = P(1 + R/100]n - P

Simple interest = PRT/100
R= 25% per annum; T and n = 3 years
Compound Interest - Simple Interest = Tk. 320

∴ [{P(1 + R/100]n - P} - (PRT/100)] = 320
⇒ [{P(1 + 25/100]3 - P} - {(P × 25 × 3)/100)}] = 320
⇒ P(5/4)3 - P - 3P/4 = 320
⇒ P(125/64) - (P + 3P/4) = 320
⇒ {(125P/64) - (7P/4)} = 320
∴ P = Tk. 1575.38

১৩.
At what rate of compound interest per annum will a sum of Tk. 1200 become Tk. 1348.32 in 2 years?
  1. ক
    ক) 7.5%
  2. খ
    খ) 6.5%
  3. গ
    গ) 7%
  4. ঘ
    ঘ) 6%
ব্যাখ্যা

Given amount = Tk. 1348.32
Principle = Tk. 1200
And time = 2 years

According to the law,
A = P(1 + R/100)n
1348.32 = 1200(1 + R/100)2
1348.32/1200 = (1 + R/100)2
11236/10000 = (1 + R/100)2
(106/100)2 = (1 + R/100)2
(1 + 6/100)2 = (1 + R/100)2
R = 6% per annum.

১৪.
A sum of Tk. 12000 deposited at compound interest become double after 5 years. After 20 years it will become ?
  1. ক
    ক) Tk. 96,000
  2. খ
    খ) Tk. 1,20,000
  3. গ
    গ) Tk. 1,24,000
  4. 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

১৫.
If the simple interest on a sum of money at 6% per annum for 4 years is Tk.1600, then find the compound interest on the same sum for the same period at the same rate.
  1. ক
    ক) Tk. 1625.35
  2. খ
    খ) Tk. 1645.45
  3. গ
    গ) Tk. 1662.35
  4. ঘ
    ঘ) Tk. 1660.66
ব্যাখ্যা

From the question, you know that R = 6%, T = 4 years, S.I. = Tk.1600

If you apply the above values in the simple interest formula S.I. = PRT/100, you will get
1600 = (P x 4 x 6)/100
⇒ P = (1600 x 100)/6 × 4
⇒ P = 6333.33

Using the above value of P, you have to now calculate C.I. as shown below:
CI = [P(1 + R/100)n] – P
= [6333.33(1 + 6/100)4] - 6333.33
= [6333.33 (106/100)4] - 6333.33
= [6333.33× 53/50 × 53/50 × 53/50 × 53/50] - 6333.33
= 7995.68 - 6333.33
= Tk.1662.35

১৬.
What is the difference between the compound interests on Tk. 5000 for 1 year at 4% per annum compound yearly and half yearly?
  1. ক
    ক) 2
  2. খ
    খ) 3
  3. গ
    গ) 2(1/2)
  4. ঘ
    ঘ) 4
ব্যাখ্যা

Interest compounded half yearly = 5000(1 + 2/100)2
= 5000(102/100)2
= 5000(1.02)2 .........(i)

As we know, A = P(1 + R/100)t
Interest compound yearly = 5000(1 + 4/100)1
= 5000(104/100)
= 5000(1.04) ............(ii)

From (i) and (ii)
Required difference = 5000(1.02)2 - 5000(1.04)1
= 5000(1.0404) - 5000(1.04)
= 5202 - 5200
= 2.

১৭.
A town had 10,000 residents in 2000. Its population declines at a rate of 10% per annum. What will be its total population in 2005?
  1. ক
    ক) 5400.50
  2. খ
    খ) 5604.71
  3. গ
    গ) 5804.81
  4. ঘ
    ঘ) 5904.90
ব্যাখ্যা

The population of the town decreases by 10% every year.
Thus, it has a new population every year. So the population for the next year is calculated on the current year population.
For the decrease, we have the formula A = P(1 - R/100)n

Therefore,
the population at the end of 5 years
= 10000(1 - 10/100)5
= 10000(1 - 0.1)5
= 10000 x 0.95
= 5904.9

১৮.
A man sells Tk. 5000, 12 % stock at 156 and invests the proceeds parity in 8 % stock at 90 and 9 % stock at 108. He hereby increases his income by Tk. 70. How much of the proceeds were invested in each stock?
  1. ক
    ক) Tk. 4000
  2. খ
    খ) Tk. 4200
  3. গ
    গ) Tk. 4002
  4. ঘ
    ঘ) Tk. 4020
ব্যাখ্যা

S.P of Tk. 5000 stock = {(156/100) × 5000}
= Tk. 7800

Income from this stock = tk. {(12/100) × 5000}
= Tk. 600

Let investment in 8 % stock be x and that in 9 % stock = (7800 - x).

Therefore,
x × (8/90) + (7800 - x) × 9/108 = 600 + 70
⇒ 4x/45 + {(7800 - x)/12} = 670
⇒ 16x + 117000 - 15x = 670 × 180
⇒ x = 3600

Money invested in 8% stock at 90 = Tk. 3600
Money invested in 9% at 108 = Tk. (7800 - 3600)
= Tk. 4200.

১৯.
12500 shares, of par value Tk. 20 each, are purchased from Ram by Mohan at a price of Tk. 25 each. Find the amount required to purchase the shares.
  1. ক
    ক) 311500
  2. খ
    খ) 312500
  3. গ
    গ) 314500
  4. ঘ
    ঘ) 313500
ব্যাখ্যা

Face value of each share = Tk.20
Market value of each share = Tk.25
Number of shares = 12500

The amount required to purchase the shares
= 12500 × 25
= 312500

২০.
A man invested Tk 1552 in a stock at 97 to obtain an income of Tk. 128 The divided from the stock is -
  1. ক
    ক) 7.5%
  2. খ
    খ) 8%
  3. গ
    গ) 8.5%
  4. ঘ
    ঘ) 9.7%
ব্যাখ্যা

By investing Tk. 1552, income = Tk. 128
By investing Tk. 97, income
= (128/1552) × 97
= Tk 8
∴ Dividend 8%.

২১.
A person invests Tk. 5508 in 4% stock at 102. He afterwards sells out at 105 and reinvests in 5% stock at 126. What is the change in his income?
  1. ক
    ক) Tk. 7
  2. খ
    খ) Tk. 9
  3. গ
    গ) Tk. 10
  4. ঘ
    ঘ) Tk. 20
ব্যাখ্যা

Number of shares purchased = 5508/102
= 54.

Income from each share = 4% of Tk. 100
= Tk. 4

∴ Original income = Tk. (54 × 4) = Tk. 216

Money incurred from sale of share = Tk. (105 × 54)
= Tk. 5670

Number of new shares purchased = 5670/126 = 45

New income = Tk. (45 × 5)
= Tk. 225

∴ Change in income = Tk. (225 - 216)
= Tk. 9.

২২.
Lopa invested a part of Tk. 12000 in 12% stock at Tk. 120 and remainder in 15% stock at Tk. 125. If his total dividend per annum is Tk. 1360, how much does he invest in 12% stock at Tk. 120?
  1. ক
    ক) Tk. 4000
  2. খ
    খ) Tk. 4500
  3. গ
    গ) Tk. 5500
  4. ঘ
    ঘ) Tk. 6000
ব্যাখ্যা

Let investment in 12% stock be Tk. x.
Then,
investment in 15% stock = Tk. (12000 - x)

∴ (12/120) × x + (15/125) × (12000 - x) = 1360
⇒ x/10 + 3/25(12000 - x) = 1360
⇒ 5x + 72000 - 6x = (1360 × 50)
⇒ x = 4000

Hence, Investment in 12% stock is Tk. 4000

২৩.
A man sells 4000 common shares of a Company x (each of par value Tk. 10), which pays a dividend of 40% at Tk. 30 per share. He invests the sale proceeds in ordinary shares of Company Y (each of par value Tk. 25) that pays a dividend of 15%. If the market value of Company Y is Tk. 15, find the number of shares of Company Y purchased by the man.
  1. ক
    ক) Tk. 16000
  2. খ
    খ) Tk. 18000
  3. গ
    গ) Tk. 12000
  4. ঘ
    ঘ) Tk. 8000
ব্যাখ্যা

Market Value of Company X (his selling price) = Tk. 30
Total shares sold = 4000

The amount he gets = Tk. (4000 × 30)
He invests this amount in ordinary shares of Company Y
Market Value of Company Y(His purchasing price) = Tk. 15

Number of shares of company Y which he purchases = (4000 × 30)/15
= Tk. 8000.

২৪.
The market value of a 10.5% stock, in which an income of Tk. 756 is derived by investing Tk. 9000, brokerage being (1/4)% is -
  1. ক
    ক) Tk. 108.25
  2. খ
    খ) Tk. 112.20
  3. গ
    গ) Tk. 124.75
  4. ঘ
    ঘ) Tk. 125.25
ব্যাখ্যা

For an income of Tk. 756, investment
= Tk. 9000

For an income of Tk. (21/2), investment
= Tk. {(9000/756) × (21/2)}
= Tk. 125

∴ For a Tk. 100 stock, investment = Tk. 125

The market value of Tk. 100 stock
= Tk. {125 - (1/4)}
= Tk. 124.75

২৫.
A invested some money in 10% stock at 96. If B wants to invest in an equally good 12% stock, he must purchase a stock worth of -
  1. ক
    ক) Tk. 80
  2. খ
    খ) Tk. 115.20
  3. গ
    গ) Tk. 120
  4. ঘ
    ঘ) Tk. 125.40
ব্যাখ্যা

For an income of Tk. 10, investment = Tk. 96
For an income of 12, investment
= Tk. (96/10) × 12
= Tk. 115.20

Hence, He must purchase a stock worth of Tk. 115.20

২৬.
A retired man sells out Tk. 7500 of a 10% stock at Tk. 105.50 and invests the proceeds in 14% stock at Tk. 124.50. What is the change in income if he pays a service charge of 0.5% of the face value on each transaction ?
  1. ক
    ক) Tk. 95
  2. খ
    খ) Tk. 114
  3. গ
    গ) Tk. 126
  4. ঘ
    ঘ) Tk. 132
ব্যাখ্যা

Number of shares sold = 7500/100
= 75

Proceeds from sale of Tk. 7500 stock
= Tk. [(105.50 - 0.5) × 75]
= Tk. 7875

Number of new shares purchased
= 7875/)124.50 + 0.50
= 7875/125
= 63

Original income
= 10% of Tk. 7500
= Tk. 750

New income
= 14% of Tk. 6300
= Tk. {(14/100) × 6300}
= Tk. 882

∴ Change in income
= Tk. (882 - 750)
= Tk. 132

২৭.
A man invests some money partly in 9% stock at 96 and partly in 12% stock at 120. To obtain equal dividends from both, he must invest the money in the ratio -
  1. ক
    ক) 3 : 4
  2. খ
    খ) 13 : 15
  3. গ
    গ) 4 : 5
  4. ঘ
    ঘ) 16 : 15
ব্যাখ্যা

For an income of Tk. 1 in 9% stock at 96,
investment = Tk. (96/9)
= Tk. 32/3

For an income of Tk. 1 in 12% stock at 120,
investment = Tk. (120/12)
= Tk. 10

Ratio of investments = (32/3) : 10
= 32 : 30
= 16 : 15.

২৮.
A man bought 40 shares of Tk. 60 at 5 discount, the rate of dividend being 12(1/2)%. The rate of interest obtained is -
  1. ক
    ক) 15.5%
  2. খ
    খ) 14%
  3. গ
    গ) 13.64%
  4. ঘ
    ঘ) 14.25%
ব্যাখ্যা

Face Value of a share = Tk. 60
He bought each share at Tk. 60 - Tk. 5 = Tk. 55
Number of shares = 40
Dividend = 12(1/2)%
= (25/2)%

Dividend per share = (60 × 25)/(2 × 100)
= Tk. 7.5

Total dividend = (40 × 7.5)
∴ He got a dividend of (40 × 7.5) for an investment of Tk. (40 × 55)

Interest obtained
= (40 × 7.5 × 100)/(40 × 55)
= 13.64%