Question

Many retirement funds charge an administrative

fee each year equal to 0.25% on managed assets.

Suppose that Alexx and Spenser each invest $5,000 in the same stock this year. Alexx invests directly and earns 5% a year. Spenser uses a retirement fund and earns 4.75%. After 30 years, how much more will Alexx have than Spenser?

Short answer

Alex earns 5% interest as he invests directly while Spenser earns 4.75%-.25%= 4.50% interest as he invests in retirement funds and they charge a 0.25% fee.

Step-by-step solution

Step 1.

In 30 years Alex earns an amount of:

$$\begin{gathered} Amount=Principal\times (1+Interestrat{e}^{time}) \\ =\$5000\times (1+0.{05}^{30}) \\ =\$5000\times 1.{05}^{30} \\ =\$21609.71 \end{gathered}$$

Step 2.

In 30 years, Spenser earns an amount of:

$$\begin{gathered} Amount=Principal\times {(1+interestrate)}^{time} \\ =\$5000\times {(1+0.045)}^{30} \\ =\$5000\times {(1.045)}^{30} \\ =\$18726.59 \end{gathered}$$

Step 3.

The difference between the amount earned by Alex and Spenser is:

$21609.71 - 18726.59 = $2883.12

So Alex will earn $2883.12 more than Spenser.