Question

Romesh borrowed a sum of Rs$245760$ at $12.5\%$ per annum, compounded annually. On the same day, he lent out his money to Ramu at the same rate of interest, but compounded semi-annually. Find his gain after $2$ years.

Answer 1

Given:

$P=$ Rs $245760$

$R=12.5\%$ p.a

$n=2$ years

When compounded annually,

We have: $A=P{(1+\frac{R}{100})}^n$

$A=245760{(1+\frac{12.5}{100})}^2$

$A=245760{\left(1.125\right)}^2$

$A=$ Rs $311040$

When compounded semi-annually,

We have:

$A=P{(1+\frac{R}{200})}^{2n}$

$A=245760{(1+\frac{12.5}{200})}^4$

$A=245760{\left(1.0625\right)}^4$

$A=$ Rs $313203.75$

Romesh’s gain $=$ Rs $313203.75–$ Rs $311040=$ Rs $2163.75$