This problem requires you to use the compound interest formula in Section 5.1. In this problem, you need to solve for *i* by removing a power.

**Problem 8** A soon to retire community college teacher wishes to have $15,000 for a motorcycle when he retires. He has $10,000 now and plans to retire in 5 years. What interest rate, compounded quarterly, will he need to earn (to the nearest tenth of a percent)? To earn full credit, you need to show the equation (see last page), all pertinent quantities and the steps you followed to solve the equation.

**Solution** Use with *PV* = 10000, *FV* = 15000 and *n* = 4∙5 and solve for *i*:

This is approximately 0.0204 or 2.04% per period. The annual rate would be four times this (quarterly!) to give 8.2%.