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Compound Interest

Q1. A sum is being lent at 30% p.a. C.I. What is the ratio of increase in amount of 4th year to 5th year ?

(a) 10:13

(b) 10:15

(c) 11:10

(d) 9:13

Solution. a
A1/A2
=
p(1 +
r/100
) 4/p(1 +
r/100
) 5
=
1/1 +
r/100
=
100/100 + r


A1/A2
=
100/130
=
10/13
= 10:13
Solution

Q2. Find the rate of interest (C.I), in which a principal becomes
25/9
times in two years.

(a) 56.66%

(b) 65.60%

(c) 66.66%

(d) 68%

Solution.c
P = x , A =
25/9
x

A = P(1 +
r/100
)n

25/9
x = x(1 +
r/100
)2

5/3
= 1 +
r/100
⇒ r = 66.66%
Solution

Q3. On a certain sum the difference between C.I & S.I for 2 years of 5% p.a. is Rs 500. Find the difference between C.I & S.I for 3 years at 5% p.a. on the same sum.

(a) 1525

(b) 1443

(c) 1123

(d)1566

Solution.a
As per question

difference between two years = 500 = P(
r/100
) 2

Now, difference between C.I & S.I for three years = P(
r/100
) 2 (
300 + r/100
)

= (500) (
300 + 5/100
) = (500)(3.05)

= 1525
Solution

Q4. At 6% p.a. SI, a certain sum becomes 3 times in a particular time of span. In the same time span, at which rate of interest the money becomes 8 times.

(a) 20%

(b) 21%

(c) 22%

(d) 25%

Solution.b
In this we apply a short trick r2 =
(n2 - 1)/(n1 - 1)
r1

r2 =
(8 - 1) x 6/(3 - 1)
=
7 x 6 /2


= 21%
Solution

Q5. Which is better investment 9% per annum compounded quarterly or 9.2% per year simple interest ?

(a) 9% p.a. compounded quarterly

(b) 9.2% per year simple interest

(c) both

(d) none

Solution.
(a) 9% p.a. compunded quarterly.
Effective rate corresponding to 9% compounded quarterly ie = (1 +
0.09/4
)4 - 1 = 9.31%
9.31% is more than 9.2%, so 9% p.a. compounded quarterly is the better investment option.
Solution