Chapter 2.6, Problem 76E

Investment problem Assume you invest $250 at the end of each year for 10 years at an annual interest rate of r. The amount of money in your account after 10 years is $A=\frac{250({(1+r)}^{10}-1}{r}$. Assume your goal is to have $3500 in your account after 10 years.

1. a. Use the Intermediate Value Theorem to show that there is an interest rate r in the interval (0.01, 0.10)—between 1% and 10%—that allows you to reach your financial goal.
2. b. Use a calculator to estimate the interest rate required to reach your financial goal.