You wish to retire in 11 years, at which time you want to have accumulated enoug

Question

You wish to retire in 11 years, at which time you want to have accumulated enough money to receive an annual annuity of $21,000 for 16 years after retirement. During the period before retirement you can earn 12 percent annually, while after retirement you can earn 14 percent on your money. What annual contributions to the retirement fund will allow you to receive the $21,000 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

Present value of annuity = P×[1-(1÷(1+r)^n)]÷r

r is interest rate per period

P is payment per period

n is number of payments

= $21,000×[1-(1÷(1+14%)^16)]÷14%

Amount required on retirement date = $131,566.25

Future value of annuity = P×[(1+r)^n-1]÷r

r is interest rate per period

P is payment per period

n is number of payments

$131,566.25 = P×[(1+12%)^11-1]÷12%

Deposit required each year for retirement goal = $6,369.83

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