Question

You want to receive $50,000 five years from today and a retirement annuity of $100,000 per year for 25 years with the first payment 10 years from today. To pay for this, you will make 5 payments of A per year beginning today and 10 annual payments of A with the first payment 8 years from today. With an interest rate of 8%, what is the value for A?

Answer #1

PV of retirement annuity received= PMT*(1-(1+r)^-n)/(r*(1+r)^10) =
100000*(1-(1+8%)^-25)/(8%*(1+8%)^10) = 494448.6817

PV of amount A paid for 5 years using annuity due formula =
(1+r)*PMT*(1-(1+r)^-n)/r = (1+8%)*A*(1-(1+8%)^-5)/8% = A*
4.3121

PV of Amount A paid for 10 years beginning 8 years from today =
A*(1-(1+r)^-n)/(r*(1+r)^8) =
A*(1-(1+8%)^-10)/8%*(1+8%)^8)=3.1081

Sum of PV of Amount Received = Sum of Amount A paid

34029.1599+494448.6817=A*(4.3121+3.1081)

A = 71221.58

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