Question

A man borrows Rs. 12500 from a bank at 20% compound interest. At the end of every year, he pays Rs. 2000 as part repayment. How much does he still owe to the bank after three such installments?

• A. Rs. 15600
• B. Rs. 12864
• C. Rs. 12000
• D. Rs. 14320

Answer 1

The correct option is D Rs. 14320

At the end of the first year, he pays 2000, therefore, he will receive interest on it for two years. At the end of the 2nd year, he pays another 2000, therefore, he will receive interest on it for 1 year. At the end of the 3rd year, he pays 2000 but he will not receive interest on it.

We know that:

$Amount=P(1+\frac{R}{100}{)}^T$

Therefore, the money he still owes to the bank after 3 years compounded anually:

$=Rs.[12500\times (1+\frac{20}{100}{)}^3]-Rs.[2000\times (1+\frac{20}{100}{)}^2+2000\times (1+\frac{20}{100})+2000]$
$=Rs.\left[\right(12500\times \frac{6}{5}\times \frac{6}{5}\times \frac{6}{5}\left)\right]-\left[\right(2000\times \frac{6}{5}\times \frac{6}{5}+2000\times \frac{6}{5}+2000\left)\right]$
$=Rs.[21600-(2880+2400+2000\left)\right]$
$=Rs.14320$