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 50000 received after 5 years = 50000/(1+8%)^5 = 34029.1599
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