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20.07.2022 - 04:36

Parents have set up a sinking fund in order to have $120,000 in 15 years for their children’s education. How much should be paid semiannually into an account paying 6.8% compounded semiannually?

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Parents have set up a sinking fund in order to have $120,000 in 15 years for their children’s education. How much should be paid semiannually into an account paying 6.8% compounded semiannually?

Answers (1)

Joanna April 1, 2023 в 20:59

The first step is to determine the present value of the $120,000 needed in 15 years. Using the formula for present value of a lump sum: PV = FV / (1 + r)^n, where PV is present value, FV is future value, r is the interest rate and n is the number of periods. PV = 120,000 / (1 + 0.068/2)^(15*2) = $41,416.06 Now, we can use the formula for the present value of an annuity due to find the semiannual payment needed to accumulate $41,416.06 in 15 years, with payments made at the beginning of each semiannual period. This formula is: PMT = PV / [(1 - (1 + r)^-n)/r(1+r)], where PMT is the payment, PV is the present value, r is the interest rate and n is the number of periods. PMT = 41,416.06 / [(1 - (1 + 0.068/2)^(-15*2))/(0.068/2)(1+0.068/2)] = $1,689.90 Therefore, the parents should make semiannual payments of $1,689.90 into an account paying 6.8% compounded semiannually in order to accumulate $120,000 in 15 years for their children's education.

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