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Question 10.EX.9: DEFERRED ANNUITY Suppose you want to retire and be able to w...

DEFERRED ANNUITY

Suppose you want to retire and be able to withdraw $40,000 per year each year for twenty years after your retirement. If you plan to stop deposits in your retirement account ten years prior to retirement, what is the balance that you must have in your retirement account ten years before you retire if you can earn 4% per year on your retirement investments?

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Balance in the account one year before retirement is the present value of an ordinary annuity with:

PMT = $40,000

N = 20

i = 4%

 

\text { Solve for } P V . P V_{\text {one year before retirement }}=\$ 543,613.05

 

Balance needed ten years before retirement:

 

P V_{10 \text { years before retirement }}=P V_{\text {one year before retirement }} \div(1+0.04)^{9} = $381,935.32

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