A college education fund is to be accumulated by twenty level semi-annual deposits, the first due on Jan. 1, 2011. The fund is to provide sixteen quarterly withdrawals of $1000 each, the first due on Oct 1, 2020. The nominal annual rate of interest is 10% convertible semi-annually. What is the amount of each deposit?

$395.74

Explanation:

the college fund requires 20 equal semiannual payments starting January 1, 2011 and the last one should be made on July 1, 2020.

first we must determine the effective rate of the fund:

effective rate = (1 + 10%/2)² - 1 = 10.25%

now we must determine the quarterly rate:

quarterly rate = (1 + r)¹/⁴ - 1 = 2.47%

the present value of the annuity:

PV = distribution x annuity factor

PV = $1,000 x 13.08553 = $13,085.53

that means that by July 1, 2020, you need to have $13,085.53 in your college fund

FV of an annuity = contribution x annuity factor

contribution = FV / annuity factor = $13,085.53 / 33.066 = $395.74

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