Question: You want to have $1,000,000 in your bank account when you turn 65 years old. Today is your 20^th birthday. As a birthday present you received $27,000 and you want to invest this amount. At what annual interest rate must you achieve to realize this goal?

Solution: We need

\[1,000,000=27,000\times {{\left( 1+r \right)}^{45}}\,\,\,\Rightarrow \,\,\,{{\left( 1+r \right)}^{45}}=37.03704\,\,\,\Rightarrow \,\,\,\,r=8.3574%\]

If not explicitly stated always assume payments are made at the end of the period.

35. The Derr-McGee Manufacturing Company plans to build a new $50,000 warehouse seven years from now. They plan to accumulate the $50,000 in an account before beginning construction. If money is worth 7% compounded annually, how much must each year?s deposit be in order to accumulate $50,000 at the end of the seventh year?