Question

Consider the following independent situations. (a) Mike Finley wishes to become a millionaire. His money market fund has a balance of \(92,296 and has a guaranteed interest rate of 10%. How many years must Mike leave that balance in the fund in order to get his desired \)1,000,000? (b) Assume that Sally Williams desires to accumulate \(1 million in 15 years using her money market fund balance of \)182,696. At what interest rate must Sally’s investment compound annually?

Short answer

The period required for Mike is 25 years, and the interest rate required for Sally will be 12%.

Step-by-step solution

Calculation of the number of years

$\begin{array}{rcl}\mathrm{Future}\mathrm{value}\mathrm{of}\$1& =& \frac{\mathrm{Desired}\mathrm{amount}}{\mathrm{Money}\mathrm{market}\mathrm{fund}\mathrm{balance}}\\ & =& \frac{100,000}{92,296}\\ & =& 10.83471\end{array}$

The future value of $1 is 10.83471 at 10% for25 years, per the table

Calculation of the interest rate

$\begin{array}{rcl}\mathrm{Future}\mathrm{value}\mathrm{of}\$1& =& \frac{\mathrm{Desired}\mathrm{amount}}{\mathrm{Money}\mathrm{market}\mathrm{fund}\mathrm{balance}}\\ & =& \frac{100,000}{182,696}\\ & =& 5.47357\end{array}$

The future value of $1 is 5.47357 for 15 years for an interest rate of12%, per the table