Question

Elena's son will enter college 16 years from now. At that time she would like to have $20,000 available for college expenses. For that purpose, her bank will set up an account that pay 7% compounded quarterly. If she makes payment into the account at the end of each quarter what must elena's payments be to achieve her goal?

Answer 1

To achieve her savings goal of $20,000 for college expenses with a bank account compounding quarterly at 7% interest, Elena must calculate the required quarterly payment using the annuity formula, substituting the known values to solve for the payment amount.

Step-by-step explanation:

Elena wants to save $20,000 for her son's college expenses with a bank account that offers a 7% interest rate compounded quarterly. Since she plans to make contributions at the end of each quarter, we can calculate the necessary payment using the future value of an annuity formula:

FV = PMT * [((1 + r/n)^(nt) - 1) / (r/n)]

Where:

• FV = Future value of the annuity (Elena's goal of $20,000)
• PMT = The payment per period (quarter) that Elena needs to find
• r = Annual interest rate in decimal (0.07 for 7%)
• n = Number of times the interest is compounded per year (4 for quarterly)
• t = The number of years the money is invested or the payments are made (16 years)

Rearranging the formula to solve for PMT, we get:

PMT = FV / [((1 + r/n)^(nt) - 1) / (r/n)]

Substituting the values:

PMT = $20,000 / [((1 + 0.07/4)^(4*16) - 1) / (0.07/4)]

Calculating the above expression will give us the quarterly payment Elena needs to make to achieve her savings goal.