Question

What equal series of payments must be paid into a sinking fund to accumulate the following amount? (a) $56,000 in 9 years at 8.85% compounded semiannually when payments are semiannual. (b) $22,000 in 14 years at 5.97% compounded quarterly when payments are quarterly. (c) $18,000 in nine years at 9.79% compounded monthly when payments are monthly. (a) The required semiannual payment amount should beRound to the nearest dollar.)

Answer 1

(a)

Semi-annual interest rate = 8.85% / 2 = 4.425%

Number of periods = 9 x 2 = 18

Semi-annual payment ($) = 56,000 / F/A(4.425%, 18) = 56,000 / 26.6694** = 2,100

(b)

Quarterly interest rate = 5.97% / 4 = 1.4925%

Number of quarters = 14 x 4 = 56

Quarterly payment ($) = 22,000 / F/A(1.4925%, 56) = 22,000 / 86.5968** = 254

(c)

Monthly interest rate = 9.79% / 12 = 0.8158

Number of months = 9 x 12 = 108

Monthly payment ($) = 18,000 / F/A(0.8158%, 108) = 18,000 / 172.2058** = 105

**F/A(4.425%, 18) = [(1.04425)¹⁸ - 1] / 0.04425 = (2.1801 - 1) / 0.04425 = 1.1801 / 0.04425 = 26.6694

**F/A(1.4925%, 56) = [(1.014925)⁵⁶ - 1] / 0.014925 = (2.2925 - 1) / 0.014925 = 1.2925 / 0.014925 = 86.5968

**F/A(0.8158%, 108) = [(1.008158)¹⁰⁸ - 1] / 0.008158 = (2.4049 - 1) / 0.008158 = 1.4049 / 0.008158 = 172.2058