A bank lends money at 12% per annum on simple interest. A customer borrows ₹ 50,000 for 9 months and repays after receiving a 5% rebate on total interest amount. What effective annual interest rate did he pay?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 11.4%
The effective annual rate is the interest actually paid, worked back to a rate for one full year. So the rebate is taken off the interest first, and the amount left is then turned into a yearly rate.
Simple interest for 9 months: \(\displaystyle 50000\times\frac{12}{100}\times\frac{9}{12}=4500\), that is ₹4,500
Rebate of 5% on it: \(\displaystyle 4500\times\frac{5}{100}=225\), that is ₹225
Interest actually paid: \(4500-225=4275\), that is ₹4,275
Effective annual rate: \(\displaystyle \frac{4275}{50000\times\frac{9}{12}}\times100=\frac{4275}{37500}\times100=11.4\%\)
Shortcut:
A 5% rebate on the interest cuts the rate itself by 5%: the borrower pays 95% of 12%
\(0.95\times12\%=11.4\%\), whatever the sum and the period