Question

A man borrows money from a finance company and has to pay it back in two equal half-yearly instalments of Rs. 5,115 each. If the interest charged by the finance company is at the rate of 20% per annum, compounded semi-annually, find the sum borrowed.

Answer 1

Each instalment = Rs. 5,115

Rate of interest = 20 % per annum = 10 % per half yearly

The amount of Rs. 5,115 paid as an instalment at the end of the first six months includes the principal and interest on it at the rate of 10 % half yearly.

Therefore,

Principal = $5115÷(1+\frac{10}{100})=Rs.4,650$

Similarly, the value which amounts to Rs. 5,115 after 1 year at the rate of 10 % compounded semi-annually is

$5115÷(1+\frac{10}{100}{)}^2=5115(\frac{100}{110}{)}^2$

$=Rs.4,227.27$

Therefore, sum borrowed = $4650+4227=Rs.8,877$ (approx.)