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jheidt1
Oct 26, 2010, 02:22 PM
You want to be a millionaire when you retire in 40 years. How much do you have to save each month if you can earn a 12% annual return? How much will you have to save if you wait 10 years?

Answer:
Today: $85
10 years: $286.13

I have a test coming up and just need to know how to solve them, I can't seem to get it right.

Thanks

ArcSine
Oct 27, 2010, 08:14 AM
The problem fits the pattern of an ordinary annuity. Google "future value of an ordinary annuity" for more insight, but the formula you need sets up as

A \ \times \ \left( \frac{(1+r)^n-1}{r} \right)

A is the amount being invested each month, n is the total number of months, and r is the monthly interest rate. Note that you are given an annual rate, so you'll need to divide it by 12.

Use the formula to verify that $84.99 and $286.12 fall just short of the target, whereas $85 and $286.12 have the legs to cross the finish line.