A loan is to be repaid in two equal yearly instalments of Rs 8112 each. If the rate of interest is 30% per annum, compounded annually, what is the total interest charged in this scheme?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Rs 5184
The loan equals the present value of the two instalments: each instalment is discounted back for the years until it is paid. The interest is what is paid in all minus the loan.
Present value of the 1st instalment \(\displaystyle =\frac{8112}{1.3}=6240\)
Present value of the 2nd instalment \(\displaystyle =\frac{8112}{1.3^{2}}=\frac{8112}{1.69}=4800\)
Loan \(=6240+4800=11040\)
Total paid \(=2\times8112=16224\)
Interest \(=16224-11040=5184\)
The total interest charged is Rs 5184.