Question

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?

* Answer to expert question. This is what was given so not sure on your question about cash flows.

Answer 1

Interest Rate = 8%

Time Period = 10 Years

Annual Series Payment = $ 5,000

Present Value of Series = $ 5,000 * PVAFdue(8%,10 years)

Present Value of Series = $ 5,000 * 7.2475

Present Value of Series(at the beginning of Year1) = $ 36,237.5

Single amount at the end of 4th year = $ 36,237.5 * FV(8%,4 Years)

Single amount at the end of 4th year = $ 36,237.5 * (1+0.08)^4

Single amount at the end of 4th year = $ 36,237.5 * 1.3605

Single amount at the end of 4th year = $ 49,300.72

Computation of PVAFdue:
r	1+r	(1+r)^-(n-1)	1- [(1+r)^-n]	[1- [(1+r)^-n]] /r	P{1+ [1- [(1+r)^-n]] /r}
8%	1.0800	0.5002	0.4998	6.2475	7.2475