Question

AISD estimates that it will need 280000 in 8 years to replace the computers in the computer labs at their high schools. if AISD establishes a sinking fund by making fixed monthly payments in to an account paying 6% compounded monthly how much should each payment be

Answer 1

The initial amount of money that must be spend to replace the computers is P = $280,000. The period of time expected to replace all the computers is t = 8 years = 96 months. The interest rate is r = 6%.

Then, the monthly payment A is given by the formula:

`\begin{gathered} A=P(r(1+r)^t)/((1+r)^t-1) \\ A=280,000\cdot(0.06\cdot(1+0.06)^(96))/((1+0.06)^(96)-1) \\ A=\text{ \$16,862.74} \end{gathered}`