A bus driver wants to earn $3,500 per year in supplemental income from an inheritance of $40,000. If the driver invests $10,000 in a mutual fund paying 8%

Question

A bus driver wants to earn $3,500 per year in supplemental income from an inheritance of $40,000.  If the driver invests $10,000 in a mutual fund paying 8%, what rate must he earn on the remainder to reach his goal?

 

Answer 1

     I'm assuming you're compounding continuously and would therefore use the formula A =P*e^rt. So,  you know 10000 at 8% for 1 year would bring in A = 10000*e^.08 = 10832.87, so he has made 832.87 in interest. He needs to make 3500-832.87 = 2667.13 on the rest of his money, 30000 or have 32667.13 in his account after the year.

 

32667.13 = 30000 *e^r    divide by 30000 

1.088904333 = e^r           take Ln of both sides

0.085171991 = r

 

So the rate on the rest of his money must be approximately 8.52%.