Question

a) When your child goes to college you want to be able to take out $500 per month from an account to help with expenses for 4 years. If your account earns 5% APR, how much will you need in the account when they start college?

b) You need to start investing now so that you have the amount from part a in an account in 15 years when your child goes to college. How much will you need to invest each month at 8% APR?

Answer 1

a]	The amount to be had in the account at the start of the 15th year = PV of the annuity due [it is presumed that the payments are to be made in the beginning of each month] of $500 per 48 months.
	The discount rate is 5%/12.
	= 500*`(1+0.05/12)*((1+0.05/12)^48-1)/((0.05/12)*(1+0.05/12)^48) =	$ 21,801.94
b]	The above amount is the FV of the amount to be
	invested monthly for 180 months, which is an annuity.
	[It is presumed that the investments are made at the
	end of each month]
	The monthly interest rate is 8%/12.
	The monthly investment required = 21801.94*(0.08/12)/((1+0.08/12)^180-1) =	$                 63.00