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What single amount, at the end of the fourth year, is equivalent to a uniform annual...

What single amount, at the end of the fourth year, is equivalent to a uniform annual series of $5,000 per year for 10 years, if the interest rate is 8% per year, compounded annually?

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Answer #1
Interest Rate = 8%
Time Period = 10 Years
Annual Series Payment = $ 5,000
Present Value of Series = $ 5,000 * PVAF(8%,10 years)
Present Value of Series = $ 5,000 * 6.71
Present Value of Series = $ 33,550
Computation of PVAF:
r 1+r (1+r)^-n 1- [(1+r)^-n] [1- [(1+r)^-n]] /r
8% 1.0800 0.4632 0.5368 6.7100
Single amount at the end of 4th year = $ 33,550 * FV(8%,4 Years)
Single amount at the end of 4th year = $ 33,550 * (1+0.08)^4
Single amount at the end of 4th year = $ 33,550 * 1.3605
Single amount at the end of 4th year = $ 45,644.41
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