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Calculating Monthly Saving for the Retirement Fund

Looking for help and how you got the answer especially on how to break out the percentages.

You wish to retire in 20 years at which time you want to accumulate enough money to receive an annual annuity of 12,000 for 25 years after retirement. During the period before retirement you can earn 8 percent annually, while after retirement you can earn 10 percent on your money.

What annual contributions to the retirement fund will allow you to receive the 12,000 annuity?

Solution Preview

If you invest x dollars every year, then in the first year your total savings will be
x dollars
in second year
x(1+.08) + x
in third year
(x(1.08)+x)(1.08) + x
and so on... for twenty years.

By the end of twentieth year you will have
20x+19*1.08x+18*(1.08^2)x+...+1*(1.08^19)x
by factoring out x, you can add it all up to get
(367.7865)*x.

This is the total dollar ...

Solution Summary

The solution contains step-by-step calculations on how much a person should save monthly in order to guarantee a specific annuity payments from the retirement fund. While specific numbers are used in the solution, the instructions are clear enough for a student to substitute his or her own numbers.

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