eco You decide to open a retirement account at your local bank that pays 10%/yea

Question

eco You decide to open a retirement account at your local bank that pays 10%/year/month (10% per year compounded monthly). For the next 20 years, you will deposit $300 per month into the account, with all deposits and withdrawals occurring at month's end. On the day of the last deposit, you will retire. Your expenses during the first year of retirement will be covered by your company's retirement plan. As such, your first withdrawal from your retirement account will occur on the day exactly 12 months after the last deposit. Click here to access the TVM Factor Table Calculator What monthly withdrawal can you make if you want the account to last 25 years? $ Round entry to the nearest dollar. Tolerance is plusminus4. What monthly withdrawal can you make if you want the account to last forever (with infinite withdrawals)? $ Round entry to the nearest dollar. Tolerance Is plusminus4.

Explanation / Answer

Solution :

The future value of annuity immediate is found using the formula

FV = A [ ( 1+r) n -1 ] / r

FV = $ 300 [ ( 1+(0.10/12)) 12X20 - 1 ] / 0.10/12

FV = $ 300 [ ( 1.0083) 240 -1 ] / 0.10/12

FV = $ 227,810.40 will be in his account at the end of 20 years by depositing $ 300 every month

This money will be in the bank account for 1 year unused and the bank pays interest for this money

At the end of 21 years the amount in the bank account = $ 227,810.40 X ( 1+(0.10/12))12 X 1

At the end of 21 years the amount in the bank account = $ 251,665.1258

The monthly withdrawl that will last for 25 years = $ 251,665.1258 / 12 X 25

The monthly withdrawl that will last for 25 years = $ 838.8837

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