Question

An article in Fortune magazine reported on the rapid rise of fees and expenses charged by mutual funds. Assuming that stock fund expenses and municipal bond fund expenses are each approximately normally distributed, suppose a random sample of 12 stock funds gives a mean annual expense of 1.63 percent with a standard deviation of .31 percent, and an independent random sample of 12 municipal bond funds gives a mean annual expense of .89 percent with a standard deviation of .23 percent. Let

Answer 1

After using the compound interest formula for 30 years, Alexx, who invested without fees and earned 5%, will have $21,609.50, while Spenser, who paid a 0.25% fee and earned 4.75%, will have $21,217.00. Thus, Alexx will have $392.50 more than Spenser after 30 years.

Step-by-step explanation:

Many retirement funds charge an annual administrative fee on managed assets. If Alexx and Spenser both invest $5,000 in the same stock and Alexx earns 5% per year without any fees while Spenser earns 4.75% per year after a 0.25% fee from a retirement fund, we need to calculate the difference in their investments' values after 30 years.

To do this, we use the formula for compound interest: Final Value = Principal × (1 + rate)time. For Alexx: Final Value = $5,000 × (1 + 0.05)30 and for Spenser: Final Value = $5,000 × (1 + 0.0475)30. After calculating these, we subtract Spenser's final value from Alexx's final value to find the difference.

For Alexx: $5,000 × 4.3219 = $21,609.50

For Spenser: $5,000 × 4.2434 = $21,217.00

Alexx will have $392.50 more than Spenser after 30 years.