You wish to retire in 12 years, at which time you want to have accumulated enoug
ID: 2621257 • Letter: Y
Question
You wish to retire in 12 years, at which time you want to have accumulated enough money to receive an annual annuity of $15,000 for 17 years after retirement. During the period before retirement you can earn 11 percent annually, while after retirement you can earn 13 percent on your money.
What annual contributions to the retirement fund will allow you to receive the $15,000 annuity? Use Appendix C and Appendix D for an approximate answer, but calculate your final answer using the formula and financial calculator methods. (Do not round intermediate calculations. Round your final answer to 2 decimal places.)
Annual Contribution:
Explanation / Answer
First of all we need to find PV of annuity at end of year 12
PV(annuity) =A*PVIFA(13%,17years)
=15000*[1-1/(1+r)^n/r]
=15000*[1-1/(1.13)^17 / 0.13]
=15000*[1-0.125/0.13]
=15000*[0.874782/0.13]
=15000*6.729093
=100936.4$
Annual contribution to be make
FV(annuity) =A [(1+r)^n-1/r]
=100936.4 = A[(1.11)^12 - 1 /0.11]
=100936.4 = A[3.49845-1/0.11]
=100936.4 = A[22.713]
A = 4443.96$
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