Question

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:

Answer 1

let the sum be = x
hope it helps

Answer 2

Answer:

sum of money = 20000

Explanation:

Let's assume that the sum of money is P.

It is given that

interest rate,r = 20%

                      = 0.2

time, t = 2 years

case i: when interest is annually, n= 1

According to the formula of compound interest,

$A_1\ =\ P(1+\dfrac{r}{n})^{nt}$  

       $=\ P(1+0.2)^2$

       = 1.44P

case ii:when interest is half yearly, n= 2

$A_2\ =\ P(1+\dfrac{r}{n})^{nt}$  

       $=\ P(1+\dfrac{0.2}{2})^4$

       = 1.4641P

According to question it is given that

   $A_2-A_1\ =\ 482$

=> 1.4641P - 1.44P = 482

=> 0.0241P = 482

=> P = 20000

Hence, the sum of money is 20000.