Question

Your younger sister is just starting high school, and 4 years from today she should be entering college. Your father plans to start a college fund for her, beginning today. He will invest $6,000 per year in a mutual fund, beginning today, and he expects to earn an annual return of 9%. What is the expected value of the college fund when your sister enters college?

a. $30,655.97
b. $29,908.26
c. $31,422.37
d. $28,431.54
e. $29,160.55

Answer 1

The expected value of the college fund after 4 years with annual contributions of $6,000 and a 9% annual rate of return, starting today, will be $28,431.54.

Step-by-step explanation:

The question given involves calculating the future value of an annuity in the context of saving for college using a mutual fund. The annuity payments are $6,000 per year and are expected to be invested at a 9% annual return, starting today.

To find the future value of the annuity due (payment at the beginning of the period), we use the formula:

FV = P × [(1 + r)^n - 1] / r × (1 + r)

Where:

FV is the future value of the annuity

P is the payment amount per period ($6,000)

r is the interest rate per period (9% or 0.09)

n is the number of periods (4 years)

By using this formula, the future value of the college fund when the sister enters college is calculated as follows:

FV = $6,000 × [(1 + 0.09)^4 - 1] / 0.09 × (1 + 0.09) = $28,431.54.

Therefore, the expected value of the college fund when your sister enters college will be $28,431.54.