Question

This is for the following two questions.

A couple plans to retire in 35 years. At that time, they would like to have enough money in an account so that they can receive a $6,000 every month end for the next 25 years. The account earns 8% APR compounded monthly and will continue to do so until there is a zero balance in the account.
To achieve this goal, how much money does the couple need to have in this account by the time they retire?
$______________(xxx.xx)
continued from above
If they have not saved any money yet, how much does the couple need to deposit each month end until they retire?
$______________(xxx.xx)

Answer 1

• $777,387.14
• $338.90

Explanation:

You want to know the value required in an account so that it can support withdrawals of $6000 per month end for 25 years, if the account earns 8% compounded monthly. And you want to know the month-end payment required into such an account to reach that value in 35 years.

Present value

The present value of an account that supports withdrawals of $6000 per month for 25 years is shown in the first calculation in the attachment. That amount is $777,387.14.

Future value

The future value of payments into the account must be that amount at the end of 35 years. The second calculation in the attachment shows that payment amount. It is $338.90.

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Additional comment

The amortization formula can be used to find the account value needed at retirement.

A = P(r/n)/(1 -(1 +r/n)^(-nt))

where A is the monthly payment, P is the needed account value, r is the annual interest rate and n=12 is the number of periods per year for t=25 years.

The monthly payment P required to achieve the account balance A can be found from the annuity formula:

A = P((1 +r/n)^(nt) -1)/(r/n)

For this, t=35 years.

In each of these cases, the equation needs to be solved for P.