Final answer:
The average rate of return on a $3,000 investment that grows at 5% for one year and 8% for three years is approximately 7.48% when compounded annually. This does not match directly with the given options.
Step-by-step explanation:
To calculate the average rate of return on an investment that grows by different rates over separate periods, we need to find the equivalent single rate that would give the same final amount if applied over the entire time period.
An investment of $3,000 grows at a rate of 5% for one year. After one year, the investment will be:
$3,000 \(\times\) (1 + 0.05) = $3,150
This amount then grows at 8% per year for three years:
$3,150 \(\times\) (1 + 0.08)3 = $3,967.30 approximately
We now need to determine the constant rate of return that would grow the original $3,000 to $3,967.30 over the 4-year period. Using the compound interest formula, where P is the principal amount, r is the rate, n is the number of times that interest is compounded per unit time period, and t is the time the money is invested or borrowed for, we can solve for the rate r.
P(1 + r)n = $3,967.30
Substitute the values we know:
$3,000(1 + r)4 = $3,967.30
(1 + r)4 = 1.32243333
1 + r = 1.07482407 (taking the fourth root)
r = 0.07482407 or 7.48% approximately
The average rate of return is not directly provided in the answer choices, so we may need to examine how the question was framed or consider rounding differences.