299+ Compound Interest Questions and Answers

Q:

A certain sum is to be divided between A and B so that after 5 years the amount received by A is equal to the amount received by B after 7 years. The rate of interest is 10%, interest compounded annually. Find the ratio of amounts invested by them.

please solve this

Answer

Let the sum(principal) received by A and B are x and y.

(1+r) = $1+\frac{1}{10}$ = $\frac{11}{10}$

Then, $\frac{x}{y}=\left ( \frac{11}{10} \right )^{7-5}$ = $\left ( \frac{11}{10} \right )^2 =\frac{121}{100}$

Hence, the ratio in which the sum is divided =121:100

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Q:

What is the rate of compound interest?
I. The principal was invested for 4 years.
II. The earned interest was Rs. 1491.

A) I alone sufficient while II alone not sufficient to answer	B) II alone sufficient while I alone not sufficient to answer
C) Either I or II alone sufficient to answer	D) Either I or II alone sufficient to answer

Answer & Explanation Answer: D) Either I or II alone sufficient to answer

Explanation:

Let Principal = Rs. P and Rate = R% p.a. Then,

Amount= $R s . [P {(1 + \frac{R}{100})}^{4}]$

C.I = $P [{(1 + \frac{R}{100})}^{4} - 1]$

$P [{(1 + \frac{R}{100})}^{4} - 1] = 1491$

Clearly, it does not give the answer

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Q:

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

A) 625	B) 635
C) 645	D) 655

Answer & Explanation Answer: A) 625

Explanation:

Let the sum be Rs. x. Then

C.I=x[1+4/100)^2-x]=[626/675x-x]

S.I=x^2/25

C.I-S.I=1

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Q:

How much money would you need to deposit today at 9% annual interest compounded monthly to have $12000 in the account after 6 years?

A) 9007	B) 4007
C) 7007.08	D) 8oo7

Answer & Explanation Answer: C) 7007.08

Explanation:

FV=P(1+r/n)^nt

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Q:

A $1000 face value Series S50 compound interest Canada Savings Bond (CSB) was presented to a credit union branch for redemption.What amount did the owner receive if the redemption was requested on:January 17, 2001?

A) 1206	B) 1306
C) 1406	D) 1506

Answer & Explanation Answer: B) 1306

Explanation:

I = ptr

Therefore, the total amount the owner received on January 17, 2001 was

$1295.57 + $10.47 = $1306.04

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Q:

The least number of complete years in which a sum of money put out at 20% C.I. will be more than doubled is ?

A) 3 years	B) 4 years
C) 2.5 years	D) 2 years

Answer & Explanation Answer: B) 4 years

Explanation:

$P {(1 + \frac{20}{100})}^{n}$ > 2P

Now, (6/5 x 6/5 x 6/5 x 6/5) > 2.

So, n = 4 years.

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Q:

Find the compound interest on Rs. 6,500 for 4 years if the rate of interest is 10% p.a. for the first 2 years and 20% per annum for the next 2 years?

A) Rs. 3845	B) Rs. 4826
C) Rs. 5142	D) Rs. 4415

Answer & Explanation Answer: B) Rs. 4826

Explanation:

We know the formula for calculating

The compound interest $C = P [{(1 + \frac{r}{100})}^{n} - 1]$ where P = amount, r = rate of interest, n = time

Here P = 5000, r1 = 10, r2 = 20

Then $C = 6500 [{(1 + \frac{10}{100})}^{2} x {(1 + \frac{20}{100})}^{2} - 1] = 6500 x \frac{1856}{2500} = \frac{65 x 1856}{25}$

C = Rs. 4826.

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Q:

What is the difference between the compound interests on Rs. 5000 for $1 \frac{1}{2}$ years at 4% per annum compounded yearly and half-yearly?

A) Rs.3.06	B) Rs.2.04
C) Rs.3.65	D) Rs.5.40

Answer & Explanation Answer: B) Rs.2.04

Explanation:

C.I. when interest compounded yearly

$R s . [5000 * (1 + \frac{4}{100}) * (1 + \frac{\frac{1}{2} * 4}{100})]$

$R s . [5000 * \frac{26}{25} * \frac{51}{50}]$

=Rs.5034

C.I. when interest iscompounded half-yearly

$R s . [5000 * {(1 + \frac{2}{100})}^{3}]$

= Rs. 5306.04

Difference = Rs. (5306.04 - 5304) = Rs. 2.04

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