You wish to retire in 12 years, at which time you want to have accumulated enoug

Question

You wish to retire in 12 years, at which time you want to have accumulated enough money to receive an annual annuity of $27,000 for 17 years after retirement. During the period before retirement you can earn 8 percent annually, while after retirement you can earn 10 percent on your money.

What annual contributions to the retirement fund will allow you to receive the $27,000 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.)

What annual contributions to the retirement fund will allow you to receive the $27,000 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.)

Explanation / Answer

To calculate the total value of accumulated amount at t=12 years,

Using the annuity formula, PV = PMT[{1-1/(1+r)^n}/r] = 27,000[{1-1/(1.1)^17/0.1] = 216,582

Now, to caculate the annual contributions required for this amount i.e. PMT

216582/[{1-1/(1.08)^12}/0.08] = $28739.5

Sorry, I took 10% on both before and after retirement. Check now?

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