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ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

পরীক্ষাব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্সতারিখতারিখ অনির্ধারিতসময়30 minutes
মোট প্রশ্ন২৫
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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 · ২৫ প্রশ্ন

১.
A company issued 20000 shares of par value Tk. 10 each. If the total dividend declared by the company is Tk. 24000, find the rate of dividend paid by the company.
  1. ক
    ক) 12%
  2. খ
    খ) 10%
  3. গ
    গ) 9%
  4. ঘ
    ঘ) 15%
ব্যাখ্যা
Number of shares = 20000
Face value of each share = Tk. 10
dividend per share = (10 × R/100) where R is the Rate of interest.
Total dividend = 20000 ×10 ×R/100
20000 ×10 ×R/100 = 24000
R = 24000/2000
= 12
Hence the dividend is 12%.
২.
Rafiq took a loan of Tk. 1600 with simple interest for as many years as the rate of interest. If he paid Tk. 256 as interest at the end of the loan period, what was the rate of interest?
  1. ক
    ক) 9%
  2. খ
    খ) 5%
  3. গ
    গ) 4%
  4. ঘ
    ঘ) 6%
ব্যাখ্যা
Simple interest is the same as the rate of interest.
Hence,
Rate of interest = R% and Time = R years

S.I. = (P × R × R)/100
⇒ 256 = (1600 × R2)/100
⇒ 16R2= 256
⇒ R2 = 16
⇒ R=4 %

Rate of Interest = 4%.
৩.
A person invests in the stock market at 10% per annum, compounded annually, for 1 years. If the interest was compounded half-yearly, he would have received Tk. 75 more. Find the sum that invest in the stock market.
  1. ক
    ক) Tk. 20,000
  2. খ
    খ) Tk. 25,000
  3. গ
    গ) Tk. 30,000
  4. ঘ
    ঘ) Tk. 35,000
ব্যাখ্যা
When interest compounded annually, then person get 10% of the total sum
If interest compounded half-annually,
Interest rate = 5% and time t = 2

As we know, 5 + 5 + (5 × 5)/100 = 10.25%
If interest compounded half-annually, then person get 10.25% of the total sum

According to the question
⇒ 10.25% – 10% = 75
⇒ 0.25% = 75
⇒ 100% = 30,000

∴ The sum that invest in the stock market = Tk. 30000
৪.
Robin invests a part of Tk. 12000 in 12% stock at Tk. 120 and the 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. 2500
  2. খ
    খ) Tk. 3500
  3. গ
    গ) Tk. 4000
  4. ঘ
    ঘ) Tk. 1500
ব্যাখ্যা
Let investment in 12% stock be Tk. x
Investment in 15% stock = 12000 – x

According to the question,
12/120 × x + 15/125 × (12000 – x) = 1360
x/10 + 3/25 (12000 – x) = 1360
5x + 72000 – 6x = 1360 × 50
x = 72,000 - 68,000
x = 4,000
৫.
A sum of money amounts to Tk. 920 in 3 years and to Tk. 1000 in 5 years. Find the rate percent per amount -
  1. ক
    ক) 3%
  2. খ
    খ) 4%
  3. গ
    গ) 5%
  4. 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%
৬.
A stock is currently at Tk. 40 per share. If the price increases by 20 percent and then decreases by 25 percent, what will be the new value of the share?
  1. ক
    ক) Tk. 41
  2. খ
    খ) Tk. 36
  3. গ
    গ) Tk. 28
  4. ঘ
    ঘ) Tk. 32
ব্যাখ্যা
First increase by 20%
So, per share value is = 40 + 40×20% = 48
Then, decrease by 25%,
So new value will become = 48 - 48×25% = 36 
৭.
Rana sells 40 shares in a company via a stock broker who charges a flat Tk. 20 commission rate on all transactions under Tk. 1000. His bank account is credited with Tk. 692 from the sale of the shares. What price were his shares sold at?
  1. ক
    ক) Tk. 15.5
  2. খ
    খ) Tk. 21.5
  3. গ
    গ) Tk. 19.5
  4. ঘ
    ঘ) Tk. 17.8
ব্যাখ্যা
কমিশনসহ রেজার শেয়ারের বিক্রয়মূল্য ৬৯২+২০ = ৭১২ টাকা।
তাহলে ৪০ শেয়ারের বিক্রয়মূল্য ৭১২/৪০ = ১৭.৮।
৮.
If a sum of money trebles itself in 20 years, what is the rate of interest?
  1. ক
    ক) 10%
  2. খ
    খ) 5%
  3. গ
    গ) 15%
  4. ঘ
    ঘ) 20%
ব্যাখ্যা
Let the sum of money be x.
x becomes 3x in 20 years.

Simple interest = 3x - x = 2x

R = (100 × 2x)/(x × 20)
   = 10%
৯.
The difference between simple and compound interest on Tk. 1400 for one year at 20% per annum reckoned half-yearly is -
  1. ক
    ক) Tk. 120
  2. খ
    খ) Tk. 3
  3. গ
    গ) Tk. 14
  4. ঘ
    ঘ) Tk. 154
ব্যাখ্যা
S.I. = (1400 × 20 × 1)/100 = Tk. 280 
C.I. = [1400 × (1 + 10/100)2 - 1400] 
      = [1400  × 11/10 × 11/10 -1400
      = 1694 - 1400
      = Tk. 294
Difference = (294 - 280) = Tk. 14.
১০.
To produce an annual income of Tk. 900 from a 9% stock at 90, the amount of stock needed is -
  1. ক
    ক) Tk. 10500
  2. খ
    খ) Tk. 10000
  3. গ
    গ) Tk. 10060
  4. ঘ
    ঘ) Tk. 18000
ব্যাখ্যা
Since face value is not given, take it as Tk. 100.
As it is an 9% stock, income (dividend) per stock = Tk. 9
ie, For an income of Tk. 9, the amount of stock needed = Tk. 100
For an income of Tk. 900, the amount of stock needed = (100 × 900)/9 = 10000
১১.
There is 90% increase in an amount in 9 years at simple interest. What will be the compound interest of Tk.1200 after 2 years at the same rate?
  1. ক
    ক) Tk. 696
  2. খ
    খ) Tk. 252
  3. গ
    গ) Tk. 196
  4. ঘ
    ঘ) Tk. 793
ব্যাখ্যা
If principal is Tk. 100
∴ Interest = 90% of Tk. 100 = Tk. 90
We know, interest, I = Pnr
Therefore, rate of interest, r = I/(Pn)
∴ Rate of Interest = 90 / (100 × 9) = 1/10 = (1/10) × 100%  = 10%
Compound interest = 1200 × (1 + 10/100)2 - 1200
                                = 1200 × 11/10 × 11/10 -1200
                                = 1452 -1200
                                = 252
১২.
A man invested Tk. 3,104 in a stock at 97 to obtain an income of Tk. 128. What is the dividend from the stock?
  1. ক
    ক) 12%
  2. খ
    খ) 9%
  3. গ
    গ) 4%
  4. ঘ
    ঘ) 10%
ব্যাখ্যা
By investing Tk. 3,104, income = Tk. 128
By investing Tk. 97, income = (128 × 97)/3104
= 4
Hence, the dividend is 4%.
১৩.
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
১৪.
Tk. 9800 are invested partly in 9% stock at 75 and 10% stock at 80 to have an equal amount of income. The investment in 9% stock is:
  1. ক
    ক) 4000
  2. খ
    খ) 4097
  3. গ
    গ) 5000
  4. ঘ
    ঘ) 5090
ব্যাখ্যা
Let the investment in 9% stock be Tk x.
Then, investment in 10% stock = Tk. (9800 - x).
(9/75) × X = 10/80 × (9800 - X)
3X/25 = (9800 - X)/8
24X = 9800 × 25 × -25X
49X = 9800 × 25
X = 5000
১৫.
A sum becomes 4 times at simple interest in 10 years. What is the rate of interest?
  1. ক
    ক) 27%
  2. খ
    খ) 25%
  3. গ
    গ) 30%
  4. ঘ
    ঘ) 35%
ব্যাখ্যা
Given: The principal(P) amount becomes 4 times at simple interest(SI) in 10 years
Formula used:
SI = (P × R × T)/100
R = rate of interest
T = time period

 According to the question:
4P = P + (P × R × T)/100
⇒ 4P = P[1 + {(R × 10)/100}]
⇒ 40 = 10 + R
⇒ R = 30

∴ Rate of interest is 30%
১৬.
In order to obtain an income of Tk. 750 from 10% stock at Tk. 96, one must make an investment of -
  1. ক
    ক) Tk. 6040
  2. খ
    খ) Tk. 6084
  3. গ
    গ) Tk. 7200
  4. ঘ
    ঘ) Tk. 6142
ব্যাখ্যা
Market Value = Tk. 96.
Required Income = Tk. 650.
Here face value is not given. Take face value as Tk. 100 if it is not given in the question
To obtain Tk. 10 (ie,10% of the face value 100), investment = Tk. 96
To obtain Tk. 650, investment = {(96/10) × 750}
= Tk. 7200.
১৭.
Samir borrows 2500 taka from a leasing company at 5% compound interest per year. Calculate the total that must be paid after 24 months.
  1. ক
    ক) 2,025.89
  2. খ
    খ) 2,756.25
  3. গ
    গ) 2,852.92
  4. ঘ
    ঘ) 2,758.78
ব্যাখ্যা
Here, n = 24 months = 2 years

Compound interest rate = 5% = 5/100

We know, C = P ( 1 + r%)2 = 2500 (1 + 5/100)2 = tk. 2,756.25
১৮.
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) 17 : 14
  2. খ
    খ) 19 : 16
  3. গ
    গ) 16 : 15
  4. ঘ
    ঘ) 18 : 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.
১৯.
If the compound interest of a certain sum of money for two successive years be Tk. 225 and Tk. 238.50 . What is the rate of interest per annum
  1. ক
    ক) 5%
  2. খ
    খ) 6%
  3. গ
    গ) 9%
  4. ঘ
    ঘ) 10%
ব্যাখ্যা
225  টাকার 1 বছরের সরল সুদ =  238.50 - 225 = 13.50  টাকা 
 
আমরা জানি,
হার = সুদ / (আসল × সময়) 
        = 13.50/(225 × 1) × 100%
         = 6%
২০.
Mobin buys 100 shares of par value Tk. 5 each, of a company, which pays an annual dividend of 12% at such a price that he gets 10% on his investment. Find the market value of a share.
  1. ক
    ক) Tk. 6
  2. খ
    খ) Tk. 8
  3. গ
    গ) Tk. 4
  4. ঘ
    ঘ) Tk. 10
ব্যাখ্যা
Face value of each share = Tk. 5
Total dividend received by Mobin = {100 × 5 × (12/100)}
= Tk. 60
Let market value of 100 shares = Tk. x
x × (10/100) = 60
x = 600
ie, Market value of 100 shares = Tk. 600
Hence, Market value of each share = Tk. 6
২১.
If the rate of simple interest is 12% per annum the amount that would fetch interest of Tk. 6,000 per annum is?
  1. ক
    ক) Tk. 45,000
  2. খ
    খ) Tk. 30,000
  3. গ
    গ) Tk. 37,000
  4. ঘ
    ঘ) Tk. 50,000
ব্যাখ্যা
Given that 
    r = 12%= 12/100
     I = Tk. 6,000
      n = 1 

We Know,
         I=Pnr 
         Pnr =I 
         P = I/nr
            = (6000×100)/12
            =50,000 Tk.
২২.
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. 117.08
  2. খ
    খ) Tk. 109.70
  3. গ
    গ) Tk. 115.20
  4. ঘ
    ঘ) Tk. 105.09
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
২৩.
A lent Tk. 5,000 to B for 2 years and Tk. 3,000 to C for 4 years on simple interest at the same rate of interest and received Tk. 2,200 in all from both of them as interest. The rate of interest per annum is:
  1. ক
    ক) 9%
  2. খ
    খ) 20%
  3. গ
    গ) 10%
  4. ঘ
    ঘ) 25%
ব্যাখ্যা
Let the rate be R%p.a.
Then,
5000 × R × 2/100 + 3000 × R × 4/100 = 2200.
⇒ 100R + 120R = 2200
⇒ R = 2200/220 =10
∴Rate = 10%
২৪.
A person has deposited Tk. 13200 in a bank which pays 14% interest. He withdraws the money and invests in Tk. 100 stock at Tk. 110 which pays a dividend of 15%. How much does he gain or lose?
  1. ক
    ক) Loses Tk. 24
  2. খ
    খ) Gains Tk. 28
  3. গ
    গ) Loses Tk. 48
  4. ঘ
    ঘ) Gains Tk. 32
ব্যাখ্যা
Income from bank = 14% of Tk. 13200 = Tk. 1848
Number of shares purchased
= Tk. (13200/110)
= Tk. 120
Income from stock
= (15% of Tk. 100) × 120
= Tk. (15 × 20)
= Tk. 1800
∴ Loss = Tk. (1848 - 1800)
= Tk. 48
২৫.
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. 120.4
  2. খ
    খ) Tk. 115.7
  3. গ
    গ) Tk. 112.50
  4. ঘ
    ঘ) Tk. 108
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