What equal series of payments must be paid into a sinking fund to accumulate the

Question

What equal series of payments must be paid into a sinking fund to accumulate the following amount? $45,000 in 10 years at 7.45% compounded semiannually when payments are semiannual. $25,000 in 15 years at 6.35% compounded quarterly when payments are quarterly. $ 12,000 in five years at 9.25% compounded monthly when payments are monthly. The required semiannual payment amount should be $ (Round to the nearest dollar.) The required quarterly payment amount should be (Round to the nearest dollar.) The required monthly payment amount should be $ (Round to the nearest dollar.)

Explanation / Answer

Let the equal periodic payment be Z in each case.

(a) Semi-annual interest rate = 7.45% / 2 = 3.725%

So,

$45,000 = Z x FVIFA(3.725%, 10) = Z x 11.8541

Z = $45,000 / 11.8541 = $3,796

(b) Quarterly interest rate = 6.35% / 4 = 1.5875%

So,

$25,000 = Z x FVIFA(1.5875%, 15) = Z x 16.7872

Z = $25,000 / 16.7872 = $1,489

(c) Monthly interest rate = 9.25% / 12 = 0.7708%

So,

$12,000 = Z x FVIFA(0.7708% x 5) = Z x 5.0777

Z = $12,000 / 5.0777 = $2,363

NOTE: If you don't have access to FVIFA table/calculator in exam, you need to use following formula to compute FVIFA manually:

FVIFA(r%, N years) = [(1 + r)N - 1] / r

(r is expressed as decimal: 10% is entered as 0.10 and not as 10)

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