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 next month, for 3 months such that your investment will grow to just cover the cost of the camp?

Answer 1

Answer:

You must invest each month, starting next month, for 3 months at a rate of 5% compounded monthly $975.36, in order to just covert the cost of the camp of your child.

Explanation:

Hi, we need to equal the future value of an annuity to the value of $1,000 per month, for 3 months in month 6, in order to pay from month 7 through 9 for the camp, using a discount rate of 5% APR, (which is 0.05/12=0.004167 or 0.4167% effective monthly). The equation we need to solve for "A" is as follows.

$\frac{A((1+0.004167)^{3}-1) }{0.004167} (1+0.004167)^{3} =\frac{1,000((1+0.004167)^{3} -1)}{0.004167(1+0.004167)^{3} }$

$A(3.050335001)=2,975.17$

$A=\frac{2,975.17}{3.050335001} =975.36$

So, you need to invest $975.36, for 3 months, starting next month, in order to pay all three months of camping, starting in month 7 (included) through month 9, at 5% APR (compounded monthly).

Best of luck.