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Monthly Payments for a Retirement Account.

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Lisa wants to retire on $56,000 per year forever. She estimates that her retirement account will earn 8.4% compounded annually. Lisa will make monthly payments into her account for the next 25 years which her company will match dollar for dollar. How much should the monthly payments be?

(Hint) What balance is needed to earn $56,000 annually from the interest? Assume that the interest rate you need is as given in the problem.

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Solution Preview

If we call M the amount she will deposit each month, then in a year she will have 12 M deposited. That amount is subject to an interest L=8.4%, so after N years its value is 12 M (1+L)^N (Here we are assuming that individual months do not have an interest associated, that is, there is an interest earned for the whole year, regardless of whether February has been more time than November, say, in the bank ). Now at the end of the second year she will have two ...

Solution Summary

We want to calculate the monthly deposit a person needs to make so that after retirement that person can live forever from interest earned only. It is assumed that the deposits are subject to a constant annually interest rate.