A loan is to be repaid in two equal yearly instalments of Rs 14553 each. If the rate of interest is 5% per annum, compounded annually, what is 75% of the total interest charged, correct to the nearest rupee?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Rs 1535
The loan equals the present value of the instalments: an instalment paid after \(n\) years is worth \(\displaystyle \frac{\text{instalment}}{(1+\frac{R}{100})^{n}}\) today. The total interest is what is paid back minus the loan.
Present value of the first instalment \(\displaystyle =\frac{14553}{1.05}=\) Rs 13860
Present value of the second instalment \(\displaystyle =\frac{14553}{1.05^{2}}=\frac{13860}{1.05}=\) Rs 13200
Loan \(=13860+13200=\) Rs 27060
Total paid \(=2\times14553=\) Rs 29106
Total interest \(=29106-27060=\) Rs 2046
75% of the interest \(=0.75\times2046=1534.5\), which is Rs 1535 to the nearest rupee
75% of the total interest is Rs 1535.