Warren Reed just turned 40. He has decided that he would like to retire when he

Question

Warren Reed just turned 40. He has decided that he would like to retire when he is 65. He thinks that he will need $1,500,000 in special retirement accounts at age 65 to maintain his current lifestyle. For the next 15 years he can afford to put $12,000 per year into the account. At age 55 he will need to withdraw $40,000 to purchase membership in the local country club. If his retirement account earns 11% compounded annually, how much will Warren need to deposit into it each year for the last ten years of his work career to attain the $1,500,000 goal?

Explanation / Answer

In order to find the amount that Warren needs to deposit when for the last 10 years, we need to find the account balance at the end of 15th year. In order to find the account balance at the end of 15th year we need to calculate the future value of an ordinary annuity (FVA). This can be determined by the following formula :

FVA = ((1+R)n -1 )/ R =

Where R is the rate of interest and n is number of years

FVA = ((1+.11)15 -1) / 0.11 = 34.4054

Since, we have FVA we can find the total value of amount if he deposits $12,000 per annum

= amount deposited per annum x FVA

= $12,000 x 34.4054 = $412,865 it is the total amount in account before club membership

Amount of club membership = $40,000

Net amount left in bank at age of 55 = $412,865 - $40,000 = $372,865

Since we have value of the balance in the account at the end of 15th year we can find the value of $372,865 at the age of 65 i.e. after 10 years.

In order to find that we need to calculate the future value factor for 10 years . This can be done by the following formula = FV = 1 x (1+r)n = 1 x (1+.11)10 = 2.83942

So, the value of $372,865 after 10 years = $372,865 x 2.83942 = $1,058,720

In order to have $1,500,000 we are short by = $441,280

This is the required accumulated value of last 10 payments

we need $441,280 more at the end of 25th year to achieve the target of $1,500,000

For that we need to find the FV of the ordinary annuity factor for 10 years = ((1+R)n - 1 )/ R = ((1+.11)10 -1) / 0.11 = 16.7220

Amount = deposit x FV of ordinary annuity

$441,280 = Deposit x 16.7220

Deposit = $441,280 / 16.7220 = $26,389

He need to make the payment of $26,389 for the last 10 years to get the amount of $ 1,500,000 in his account.

Hope this helps.

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