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 245, 760
R = 12 . 5 % p . a .
n = 2 years
When compounded annually, we have:
\[A = P \left( 1 + \frac{R}{100} \right)^n \]
 = Rs \[245, 760 \left( 1 + \frac{12 . 5}{100} \right)^2 \]
 = Rs \[311, 040\]
When compounded semi - annually, we have: 
\[A = P \left( 1 + \frac{R}{200} \right)^{2n} \]
 = Rs \[245, 760 \left( 1 + \frac{12 . 5}{200} \right)^4 \]
= Rs \[245, 760 \left( 1 . 0625 \right)^4 \]
 = Rs 313, 203 . 75
Romesh's gain = Rs 313, 203 . 75 - Rs 311, 040
 = Rs 2, 163 . 75