Question

your wonderful parents established a college savings plan for you when you were born. They deposited $50 into the account on the last day of each month. The account has earned 10% compounded monthly. Now you are off to Monash university. What equal amount can they withdraw beginning today (your 18th birthday) and each year for 4 years to spend on your education, assuming that the account now earns 7% annually?

Answer 1

1]	Accumulated value of the monthly savings [annuity] = FV of the annuity = 50*((1+0.10/12)^216-1)/(0.10/12) =	$          30,028.16
2]	The annual withdrawals are an annuity due. The above amount is
	the PV of the annuity due. Hence, the annuity is:
	= 30028.16*0.07*1.07^4/((1.07)*(1.07^4-1) =	$            8,285.19
	Formulae used:
	FV of annuity = A*((1+r)^n-1)/r
	where,
	A = Annuity
	r = rate of interest [here, per month of 10%+12]
	n = number of periods [here, 18*12 = 216 months]
	PV of annuity due:
	PV = A*((1+r)^n-1)*(1+r)/((r)*(1+r)^n)
	The above formula is adapted to get A
	A = PV*r*(1+r)^n/((1+r)^n-1)*(1+r)