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?

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.

The amount used= 13.04- 1.9 = 11.14