Question

A certain sum is given on compound interest at some rate. the sum amounts to 7350 and 8575 at the end of 2 years and 3 years respectively.the sum given on compound interest is

Answer 1

Answer: The sum given on compound interest is 5400.

We follow these steps to arrive at the answer:

Let the sum given on compound interest be P

The compound interest formula is:

$FV = P(1+r)^{n}$ where

FV is the total amount received along with interest at the end of the stated period,

r is the interest rate per period

n is number of periods

Plugging the values given in the question in the formula above we get,

$7350 = P* (1+r)^{2}$  ----- 1                   and

$8525 = P* (1+r)^{3}$  ----- 2

Dividing 2  by 1 we get,

$\frac{8525}{7350} = \frac{P* (1+r)^{3}{P* (1+r)^{2}$

$1.166666667 = (1+r)$

Substituting the value of (1+r) above in 1 we get,

$7350 = P * (1.166666667)^{2}$

$\frac{7350}{(1.166666667)^{2}} = P$

$P = 5400$

Answer 2

interest of third year = 8575 - 7350 = 1225  

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

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

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 %