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A couple saves $500.00 per month (end of month) for 40.00 years. They can earn 6.00%...

A couple saves $500.00 per month (end of month) for 40.00 years. They can earn 6.00% annual interest with monthly compounding on this account. The couple wants their retirement account to last for 25.00 years. When they retire, they will move their savings into a money market fund that pays 2.40% annual interest with monthly compounding.

What is the value of this account when they retire?

Assuming they withdraw at the beginning of the month, what monthly withdrawals will this account support?

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Answer #1

This question requires application of concept of annuities.

FV of annuity deposits made by couple can be calculated using the formula:

n = 40*12 months = 480 months, r = 6%/12 = 0.5% (monthly)

FV = $955,745.37--> Value of account at retirement

This would now be the present value of annuity of withdrawals that will take place for 25 years (25 * 12 = 300 months) at rate of 2.4% (=2.4%/12 = 0.2% monthly rate)

P = $4,417.10 --> Monthly payment that they can withdraw during retirement

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