# Compound Interest Questions

FACTS  AND  FORMULAE  FOR  COMPOUND  INTEREST  QUESTIONS

Let Principal = P, Rate = R% per annum, Time = n years.

I.

1.  When interest is compound Annually:

Amount =$P{\left(1+\frac{R}{100}\right)}^{n}$

2.  When interest is compounded Half-yearly:

Amount = $P{\left[1+\frac{\left(R}{2}\right)}{100}\right]}^{2n}$

3.  When interest is compounded Quarterly:

Amount = $P{\left[1+\frac{\left(R}{4}\right)}{100}\right]}^{4n}$

II.

1.  When interest is compounded Annually but time is in fraction, say $3\frac{2}{5}$ years.

Amount = $P{\left(1+\frac{R}{100}\right)}^{3}×\left(1+\frac{\frac{2}{5}R}{100}\right)$

2.  When Rates are different for different years, say R1%, R2%, R3% for 1st, 2nd and 3rd year respectively.

Then, Amount = $P\left(1+\frac{{R}_{1}}{100}\right)\left(1+\frac{{R}_{2}}{100}\right)\left(1+\frac{{R}_{3}}{100}\right)$

III.  Present worth of Rs. x due n years hence is given by:

Present Worth = $\frac{x}{{\left(1+\frac{R}{100}\right)}^{n}}$

Q:

Find compound interest on Rs. 8000 at 15% per annum for 2 years 4 months, compounded annually

 A) 2109 B) 3109 C) 4109 D) 6109

Explanation:

Time = 2 years 4 months = 2(4/12) years = 2(1/3) years.
Amount = Rs'. [8000 X (1+(15/100))^2 X (1+((1/3)*15)/100)]
=Rs. [8000 * (23/20) * (23/20) * (21/20)]
= Rs. 11109. .
:. C.I. = Rs. (11109 - 8000) = Rs. 3109.

91 30825
Q:

A sum of money lent at compound interest for 2 years at 20% per annum would fetch Rs.482 more, if the interest was payable half yearly than if it was payable annually . The sum is

 A) 10000 B) 20000 C) 40000 D) 50000

Explanation:

Let sum=Rs.x

C.I. when compounded half yearly = $\left[x{\left(1+\frac{10}{100}\right)}^{4}-x\right]=\frac{4641}{10000}$

C.I. when compounded annually =$\left[x{\left(\frac{20}{100}\right)}^{2}-x\right]=\frac{11}{25}$

$\frac{4641}{10000}x-\frac{11}{25}x=482$

=> x=20000

103 29209
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

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 = $Rs.\frac{100*200}{8*1}$ = Rs.2500

Amount for 2 years, compounded half-yearly

$Rs.\left[2500*{\left(1+\frac{4}{100}\right)}^{4}\right]=Rs.2924.4$

C.I = Rs.424.64

Also, $S.I=Rs.\left(\frac{2500*8*2}{100}\right)=Rs.400$

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

33 22876
Q:

A sum of money amounts to Rs.6690 after 3 years and to Rs.10,035 after 6 years on compound interest.find the sum.

 A) 4360 B) 4460 C) 4560 D) 4660

Explanation:

Let the sum be Rs.P.then
P(1+R/100)^3=6690…(i) and P(1+R/100)^6=10035…(ii)
On dividing,we get (1+R/100)^3=10025/6690=3/2.
Substituting this value in (i),we get:
P*(3/2)=6690 or P=(6690*2/3)=4460
Hence,the sum is rs.4460.

59 22103
Q:

The compound interest on rs.30000 at 7% per annum is Rs.4347. The period is

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

Explanation:

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

let the time be n years

Then,30000(1+7/100)^n = 34347

(107/100)^n = 34347/30000 = 11449/10000 = (107/100)^2

$\inline \fn_cm \therefore$n = 2years

32 18596
Q:

What is the rate of interest p.c.p.a.?

I. An amount doubles itself in 5 years on simple interest.

II. Difference between the compound interest and the simple interest earned on a certain amount in 2 years is Rs. 400.

III. Simple interest earned per annum is Rs. 2000

 A) I only B) II and III only C) All I, II and III D) I only or II and III only

Answer & Explanation Answer: D) I only or II and III only

Explanation:

$I.\frac{P*R*5}{100}=P⇔R=20$

$II.P{\left(1+\frac{R}{100}\right)}^{2}-P-\frac{P*R*2}{100}=400=>p{R}^{2}=4000000$

$III.\frac{P*R*1}{100}=2000=>PR=200000$

$\frac{P{R}^{2}}{PR}=\frac{4000000}{200000}⇔R=20$

Thus I only or (II and III) give answer.

36 17000
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

Explanation:

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

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

Simple Interest on P at 10% for 2 years = $\frac{PRT}{100}=\frac{P×10×2}{100}=\frac{P}{5}$

Given that difference between compound interest and simple interest = 124.05

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

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

P=8000

17 16668
Q:

Find the compound interest on Rs. 10,000 in 2 years at 4% per annum, the interest being compounded half-yearly.

 A) 524.32 B) 624.32 C) 724.32 D) 824.32

Explanation:

Principal = Rs. 10000; Rate = 2% per half-year; Time = 2 years = 4 half-years.
Amount == Rs. 10824.32.

$Rs.\left[10000*{\left(1+\frac{2}{100}\right)}^{4}\right]=Rs.\left[10000*\frac{51}{50}*\frac{51}{50}*\frac{51}{50}*\frac{51}{50}\right]$

$\inline \therefore$ C.I. = Rs. (10824.32 - 10000) = Rs. 824.32.