You wish to retire in 15 years, at which time you want to have accumulated enoug
ID: 2681796 • Letter: Y
Question
You wish to retire in 15 years, at which time you want to have accumulated enough money to receive an annual annuity of $18,000 for 20 years after retirement. During the period before retirement you can earn 9 percent annually, while after retirement you can earn 11 percent on your money.What annual contributions to the retirement fund will allow you to receive the $18,000 annuity? Use Appendix C and Appendix D. (Round "PV Factor" and "FV Factor" to 3 decimal places and final answer to 2 decimal places. Omit the "$" sign in your response.)
Annual contribution $
Explanation / Answer
We can think of retirement as its own timeline, and calculate the present value of the 18,000 annuity. This will give us how much money he will need to save up prior to retiring; PMT = 18000 N = 20 years i = 0.11 Present Value of an Annuity; PVoa = PMT [(1 - (1 / (1 + i)^n)) / i] PVoa = 18000 [(1 - (1 / (1 + 0.11)^20)) / 0.11] PVoa = 12000 * 7.9633 = $95559.6 Now, if we look at pre-retirement as it's own timeline, we need to accumulate 95559.6 dollars at the end using an annuity of some payment. FV = 95559.6 i = 0.09 N = 15 Future Value of an Annuity; FVoa = PMT [((1 + i)^n - 1) / i] 108,924.48 PMT [((1 + 0.09)^15 - 1) / 0.09] 108,924.48 = PMT * 29.3609 PMT = 3709.848 $3709.85 is the required payment
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