Suppose $5000 is invested in a savings account for 10 years (120 months), with an annual interest rate of r, compounded monthly. The amount of money in the account after 10 years is A(r) = 5000(1 + r/12)¹²⁰.

a. Use the Intermediate Value Theorem to show there is a value of r in (0, 0.08)—an interest rate between 0% and 8%—that allows you to reach your savings goal of $7000 in 10 years.

b. Use a graph to illustrate your explanation in part (a); then approximate the interest rate required to reach your goal.