Question

Rahul borrowed rs. 1,00,000 @ 8% p.a. compound interest, interest being compounded annually. ow much should he repay at the end of the first year, so that by repaying rs. 54,000 at the end of the second year he can clear the loan ?

Answer 1

Rahul borrowed rs 100000 @ 8% p.a.compound interest being compound annually is 8000

Answer 2

Rs. 58000 is the amount of money paid in the first year.

Given:

Rahul borrowed = Rs.1,00,000  

Interest = 8%

Repaying amount in the second year = Rs.54,000

To find:

Amount to repay at the end of the first year =?

Solution:

The sum or principal (P) of money borrowed was Rs. 100000

The rate (R) at which the money was borrowed was 8% compounding annually  

The time (t) for which the money was borrowed was 2 years

The Amount obtained till the first haft of the second year is $A=P\left(1+\frac{8}{100}\right)^{\frac{3}{2}}$

$A=100000\left(1+\frac{8}{100}\right)^{\frac{3}{2}}$

A=Rs.112000  

Now, the amount of money repaid at the end of the 2 years is Rs. 54000

Therefore, the amount paid until the first half of the 2nd year is Rs. (Rs. 112000 – 54000 = Rs.58000)

Hence, the amount of money paid in first year is Rs. 58000.