Question

Mr. Raju lent out a certain sum on simple interest and the same sum on compound interest at a certain rate
of interest per annum. If the ratio between the difference of compound interest and simple interest of 2
years and that of 3 years is 10:31, what is the rate of interest per annum?
7.5%
10
15%
12.5%​

Answer 1

Given : Mr. Raju lent out a certain sum on simple interest and the same sum on compound interest at a certain rate  of interest per annum.

the ratio between the difference of compound interest and simple interest of 2  years and that of 3 years is 10 : 31

To Find  : what is the rate of interest per annum

Solution:

Let say Amount = 100P

Simple interest in 2Years  = 100P *  R * 2 / 100  =  2PR

Compound interest in 2 Years = 100P(1 + R/100)²  - 100P

= 100P ( R²/100²  + 2R/100)

= 2PR   +   P R²/100

Difference in Interest in 2 Years = 2PR   + P R²/100  -  2PR

=   P R²/100

Simple interest in 3Years  = 100P *  R * 3 / 100  =  3PR

Compound interest in 3 Years = 100P(1 + R/100)³  - 100P

= 100P ( 1 + R³/100³ + 3R²/100² + 3R/100)  - 100P

= PR³/100² + 3PR²/100 + 3PR

Difference on interest in 3 Years =  PR³/100² + 3PR²/100 + 3PR  -   3PR

= PR³/100² + 3PR²/100

= PR²/100( R/100 + 3)

 (P R²/100 ) / (P R²/100)( 3 + R /100)   = 10/31

=> 31 =  10 ( 3 + R/100)

=> 31 = 30  + R/10

=>  1 = R/10

=>  R =  10

rate of interest per annum = 10 %

Taking P = 100

Year           SI                   CI                   Difference

1                 10                    10                  0

2                20                   21                   1    

3                30                 33.1                 3.1    

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