Question

Rakesh lent out Rs 10000 for 2 years at 20% per annum, compounded annually. How much more he could earn if the interest be compounded half-yearly?

Answer 1

Given: 
P = Rs 10, 000
R = 20 % p. a.
n = 2 years
\[A = P \left( 1 + \frac{R}{100} \right)^n \]
 = Rs \[10, 000 \left( 1 + \frac{20}{100} \right)^2 \]
 = Rs \[10, 000 \left( 1 . 2 \right)^2 \]
 = Rs 14, 400
When the interest is compounded half - yearly, we have: 
\[A = P \left( 1 + \frac{R}{200} \right)^{2n} \]
= Rs \[10, 000 \left( 1 + \frac{20}{200} \right)^4 \]
 = Rs \[10, 000 \left( 1 . 1 \right)^4 \]
 = Rs 14, 641
Difference = Rs 14, 641 - Rs 14, 400
 = Rs 241