Question

Problem 3.9 John wants to have $800. He may obtain it by promising to pay $900 at the end of one year; or he may borrow $1,000 and repay $1,120 at the end of the year. If he can invest any balance over $800 at 10% for the year, which should he choose?

Answer 1

Option (a) If John borrows $800 and pays $900 at end of an year, interest rate = (900-800)/800 *100% = 12.5%

Option (b) If John borrows $1000 and repays $1120 at end of year, interest rate = (1120-1000)/1000 * 100% = 12%

Option (c) If he borrows $1000, of which he invests $200 (balance above $800) at 10%, returns received in 1 year = 200*10/100 = $20

Hence, he borrows $1000, uses $800 and invests $200. He earned $20 and hence has to repay 1100. Hence, applicable interest rate in this scenario = (1100-1000)/1000 *100 = 10%

Hence, the best option is to borrow $1000, and invest $200