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Rayelle’s parents plan to invest $15,000 in a mutual fund earning an average of 4.5 percent interest, compounded monthly. After 15 years, for how many years will this investment be able to cover the tuition, fees, room, and board for Rayelle at a public college if costs stay the same? Round your answer to the nearest month

User Burunoh
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Answer + Explanation:

To calculate how many years the investment will be able to cover Rayelle's college costs, we need to know the annual cost of tuition, fees, room, and board at a public college. Let's assume that this cost is $20,000 per year.We also need to know the future value of the investment after 15 years. Using the compound interest formula, we can calculate that the future value of the investment will be:

FV = PV * (1 + r/12)^(n*12)

where PV is the present value of the investment, r is the annual interest rate, n is the number of years, and FV is the future value of the investment.Plugging in the numbers, we get:

FV = $15,000 * (1 + 0.045/12)^(15*12) = $29,286.95

So, after 15 years, the investment will be worth $29,286.95.To calculate how many years the investment will be able to cover Rayelle's college costs, we can divide the future value of the investment by the annual cost of college, and then divide by 12 to get the number of years in months. This gives us:

Years = FV / (Annual cost of college) / 12

Years = $29,286.95 / $20,000 / 12 = 12.24 years

So, the investment will be able to cover Rayelle's college costs for approximately 12 years and 3 months. Rounded to the nearest month, the answer is 147 months. Therefore, the investment will be able to cover Rayelle's college costs for about 147 months.

Hope this helps!

- Dante

User EzioMercer
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