You would like to have $4,500 in 3 years for a special vacation following gradua

Question

You would like to have $4,500 in 3 years for a special vacation following graduation by making deposits at the end of every six months in an annuity that pays 5.5% compounded semiannually Determine how much you should deposit at the end of every six months. b. How much of the $4,500 comes from deposits and how much comes from interest? a. In order to have $4,500 in 3 years, you should deposit at the end of every six months. (Do not round until the final answer. Then round up to the next dollar.) b. Sof the (Use the answer from part a to find this answer. Round to the nearest dollar as needed.) 4.500 comes from your deposits and s comes from interest

Explanation / Answer

The formula for computing the future value (F) of an annuity is F = P[(1 + r)n - 1)/ r], where P is the periodic payment, r is the interest rate per period and n is the number of periods.

a.Here, F = $ 4500, n = 3*2 = 6, and r = 5.5/100 = 0.055. Then, 4500 = P[(1.055)6 -1]/0.055 or, P = 4500*0.055/[(1.055)6 -1] = 245.5 /0.378842806 = $ 649 ( on rounding off to the nextdollar). Thus, in order to have $ 4500 in 3 years, one should deposit $ 649 at the end of every 6 months.

b. Since $ 649 *6 = $3894, hence $ 3894 comes from one’s deposits and $ 4500 -$ 3894 = $ 606 comes from interest.

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