Question 1093808
<br>Ooh! A present value formula for working a problem involving compound interest.  Certainly valid; but not easy to understand, so not the way I would go.<br>
You are starting with some unknown amount x.
The money is accruing interest monthly for 9 years; that is 9*12 =108 months.
The annual interest rate is 5%, or .05; the periodic (monthly) interest rate is one-twelfth of that, let's just call it (.05/12).
The "growth factor" -- what the value of the account gets multiplied by each time interest is gained, is 1 plus the periodic interest rate; in this case (1+.05/12).
The growth factor is applied to the beginning amount 108 times (monthly for 9 years).<br>
So, since we want the value after the 9 years to be $20,000,
{{{20000 = x(1+.05/12)^108}}}
{{{x = 20000/((1+.05/12)^108) = 12764.49}}}