Question

Your child is planning attend summer camp for three months, starting 7 months from now. The cost for camp is $1,000 per month, each month, for the three months she will attend. If your investments earn 5% APR (compounded monthly), how much must you invest each month, starting two months from now, for 3 months such that your investment will grow to just cover the cost of the camp?

$1,000

$1,004

$979

$996

Answer 1

Present value = Future value/(1+i)^n

i = interest rate per period

n= number of periods

Present value of deposits and payments = 0

=>

x/(1+0.05/12)^2 + x/(1+0.05/12)^3 + x/(1+0.05/12)^4  - 1000/(1+0.05/12)^7 - 1000/(1+0.05/12)^8 - 1000/(1+0.05/12)^9 = 0

=>

x * [1/(1+0.05/12)^2 + 1/(1+0.05/12)^3 + 1/(1+0.05/12)^4] =  2901.8659772

= 979.43

= 979