Matt's parents decide to set up a college fund on his 10th birthday. They would like for the fund to be worth $36,273 on his 18th birthday. The make semi-annual payments into an account earning interest at an annual rate of 4.4%, compounded semi-annually. Find the size of the semi-annual payments required in order for the parents to have saved the desired amount by Matt's 18th birthday. Find the total amount deposited by the parents. As of Matt's 18th birthday, find the total amount of interest earned by the account. Enter the answer to Part c in the box below. Round your answer to the nearest dollar.

a. $1,916.00

b. $‭30,656‬

c. $‭7,617‬

Explanation:

a. As they are depositing a set amount every 6 months, this is an annuity. The $36,273 is the future value of the annuity in 8 years.

n = 8 years * 6 = 16 semi annual periods

rate = 4.4/ 2 = 2.2% every 6 months

Future value = Amount * (([1 + i]^n) - 1 )/i

36,273 = Amount * (([1 + 2.2%]^16) - 1 )/2.2%

36,273 = Amount * 18.931485

Amount = 36,273/18.931485

= $1,916.00

b. Total amount deposited

= 16 * 1,916

= $‭30,656‬

c. Total amount of interest earned;

= Amount in fund - Total deposited

= 38,273 - 30,656

= $‭7,617‬

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