# 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:

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

n = 2years

266 79384
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.

188 59993
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 = $x1+101004-x=464110000$

C.I. when compounded annually =$x201002-x=1125$

$464110000x-1125x=482$

=> x=20000

243 52690
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.

296 52674
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:

$I.P*R*5100=P⇔R=20$

$II.P1+R1002-P-P*R*2100=400=>pR2=4000000$

$III.P*R*1100=2000=>PR=200000$

$PR2PR=4000000200000⇔R=20$

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

69 42978
Q:

Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?

 A) 3.6 B) 6 C) 18 D) Cannot be determined

Explanation:

Explanation:

Let rate = R% and time = R years.

Then, $1200*R*R100=432$

$12R2=432$

=>$R2=36⇔R=6$

87 42925
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.

$Rs.10000*1+21004=Rs.10000*5150*5150*5150*5150$

C.I. = Rs. (10824.32 - 10000) = Rs. 824.32.

112 42078
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 = $Rs.100*2008*1$ = Rs.2500

Amount for 2 years, compounded half-yearly

$Rs.2500*1+41004=Rs.2924.4$

C.I = Rs.424.64

Also, $S.I=Rs.2500*8*2100=Rs.400$

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