Question

In the aftermath of the mortgage crisis, Phil and Crystal, are considering remodeling their home. They originally wanted to sell their home and move to another area, but news shows a decline in real estate values. Their plan now is to improve their home’s curb appeal as well as update the interior. They estimate the cost will be $86,000.

How much must they invest today at 6% interest compounded quarterly to have the money they need to remodel in 8 years?

Answer 1

If present amount P earns interest at annual rate r compounded n times per year for t years, the future amount A will be ...
A = P*(1 +r/n)^(nt)

Put the numbers you know in the formula, and solve for the one you don't know.
86000 = P*(1 +.06/4)^(4*8)
86000 = P*1.61032432
86000/1.61032432 = P ≈ 53,405.39

Phil and Crystal must invest $53,405.39 to reach their investment goal.

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A TI-84 calculator has a time-value-of-money (TVM) solver useful for problems like this.