299+ Compound Interest Questions and Answers

Q:

Find compound interest on Rs. 7500 at 4% per annum for 2 years, compounded annually.

A) 612	B) 712
C) 812	D) 912

Answer & Explanation Answer: A) 612

Explanation:

Amount = Rs [7500*(1+(4/100)2] = Rs (7500 * (26/25) * (26/25) ) = Rs. 8112.
therefore, C.I. = Rs. (8112 - 7500) = Rs. 612.

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Q:

There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of Rs. 12,000 after 3 years at the same rate

A) Rs.4972	B) Rs.3972
C) Rs.5972	D) Rs.2972

Answer & Explanation Answer: B) Rs.3972

Explanation:

Let P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years.

R= $\frac{100 * 60}{100 * 6}$ =10% p.a

Now, P = Rs. 12000. T = 3 years and R = 10% p.a.

C.I= $R s . [12000 * {[1 + \frac{10}{100}]}^{3} - 1]$
=Rs.3972

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Q:

The difference between compound interest and simple interest on a sum for two years at 8% per annum, where the interest is compounded annually is Rs.16. if the interest were compounded half yearly , the difference in two interests would be nearly

A) Rs.24.64	B) Rs.21.85
C) Rs.16	D) Rs.16.80

Answer & Explanation Answer: A) Rs.24.64

Explanation:

For 1st year S.I =C.I.

Thus, Rs.16 is the S.I. on S.I. for 1 year, which at 8% is thus Rs.200

i.e S.I on the principal for 1 year is Rs.200

Principle = $R s . \frac{100 * 200}{8 * 1}$ = Rs.2500

Amount for 2 years, compounded half-yearly

$R s . [2500 * {(1 + \frac{4}{100})}^{4}] = R s . 2924.4$

C.I = Rs.424.64

Also, $S . I = R s . (\frac{2500 * 8 * 2}{100}) = R s . 400$

Hence, [(C.I) - (S.I)] = Rs. (424.64 - 400) = Rs.24.64

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Q:

If the simple interest on a sum of money at 5% per annum for 3 years is Rs. 1200, find the compound interest on the same sum for the same period at the same rate.

A) 1261	B) 1271
C) 1281	D) 1291

Answer & Explanation Answer: A) 1261

Explanation:

Clearly, Rate = 5% p.a., Time = 3 years, S.I.= Rs. 1200. . .
So principal=RS [100*1200]/3*5=RS 8000
Amount = Rs. 8000 x [1 +5/100]^3 - = Rs. 9261.
.. C.I. = Rs. (9261 - 8000) = Rs. 1261.

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Q:

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

A) 2.04	B) 3.04
C) 4.04	D) 5.04

Answer & Explanation Answer: A) 2.04

Explanation:

C.I. when interest
compounded yearly=rs.[5000*(1+4/100)(1+1/2*4/100)]

= Rs. 5304.

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

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

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Q:

A certain sum amounts to Rs.7350 in 2 years and to Rs.8575 in 3 years.find the sum and rate percent

A) 3400	B) 4400
C) 5400	D) 6400

Answer & Explanation Answer: C) 5400

Explanation:

Interest for 1 year is the same whether it's simple interest or the compound interest.

Now interest of third year = 8575 - 7350 = 1225; means principal for this interest is 7350 if comound interest is takenIf 7350 is the principal interest = 1225

if 100 is the principal interest =(1225/7350) * 100 = 50/3 %

When a thing increases for two successive times the overall increase on initial amount = a + b + (a * b)/100

Therefore overall interest for two years = 50/3 + 50/3 + [(50/3)*(50/3)]/100 = 325/9 %

Therefore amount after 2 years = 100 + 325/9 = 1225/9

If 1225/9 is the amount principal =100

if 7350 is the amount principal =(900/1225)*7350 =5400

So sum = 5400; Rate = 50/3 %

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Q:

On a sum of money, the simple interest for 2 years is Rs. 660,while the compound interest is Rs.696.30,the rate of interest being the same in both the cases. The rate of interest is

A) 10%	B) 11%
C) 12%	D) 13%

Answer & Explanation Answer: B) 11%

Explanation:

Difference in C.I and S.I for 2 years

= Rs(696.30-660)

=Rs. 36.30.

S.I for one years = Rs330.

S.I on Rs.330 for 1 year =Rs. 36.30

Rate

= (100x36.30/330x1)%

= 11%

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Q:

The difference between the simple interest on a certain sum at the rate of 10%per annum for 2 years and compound interest which is compounded every 6 months is Rs.124.05. what is the principal sum

A) Rs.6000	B) Rs.8000
C) Rs.12000	D) none of these

Answer & Explanation Answer: B) Rs.8000

Explanation:

Compound Interest on P at 10% for 2 years when interest is compounded half-yearly

= $P {(1 + \frac{\frac{R}{2}}{100})}^{2 T} - P = P {(1 + \frac{1}{20})}^{4} - P = P {(\frac{21}{20})}^{4} - P$

Simple Interest on P at 10% for 2 years = $\frac{P R T}{100} = \frac{P \times 10 \times 2}{100} = \frac{P}{5}$

Given that difference between compound interest and simple interest = 124.05

$P * {(\frac{21}{20})}^{4} - P - \frac{P}{5} = 124.05$

=> $P [{(\frac{21}{20})}^{4} - 1 - \frac{1}{5}] = 124.05$

P=8000

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