Question

Jaide and Jim plan to send their daughter Sarah (currently 7-year old) to university at the age of 18 for a 4-year undergraduate program in Ontario Tech. University. They intend to invest ANNUALLY in a GIC account, which pays 3.5% interest per year. That is, the first annual deposit occurs today (i.e. 7th birthday) until she turns 17. The university tuition currently is $8,000 per year. It is estimated that the tuitions grow at the inflation rate (2% per year). Tuitions will be paid at the beginning of each year (i.e. when Sarah is 18,19,20, and 21). Assume there is no tax to be paid on the account upon withdrawal. How much should the parents save each year to be able to fully fund their daughter’s university tuition expenses?

Answer 1

Fees currently-T7	$ 8,000
Inflation rate per annum	2%
Fees at T18	8000*(1+2%)^11	$ 9,946.99
Fees at T19	8000*(1+2%)^12	$10,145.93
Fees at T20	8000*(1+2%)^13	$10,348.85
Fees at T21	8000*(1+2%)^14	$10,555.83
Lets compute the PV of these fees payments at T17.
		PV factor, 1/(1+3.5%)^t	PV= Payment * PV factor
Fees at T18	$         9,946.99	1.000	$ 9,946.99
Fees at T19	$       10,145.93	0.966	$ 9,802.84
Fees at T20	$       10,348.85	0.934	$ 9,660.77
Fees at T21	$       10,555.83	0.902	$ 9,520.75
		Total PV	$38,931.35
So now lets make an annuity so that the future value of annuity is $ 38,931.35
FV of annuity due
P = PMT x ((((1 + r) ^ n) - 1) / r)*(1+r)
Where:
P = the future value of an annuity stream		$38,931.35
PMT = the dollar amount of each annuity payment	To be computed
r = the effective interest rate (also known as the discount rate)	3.50%
n = the number of periods in which payments will be made	11
	38931.35=	PMT x ((((1 + r) ^ n) - 1) / r)*(1+r)
	38931.35=	PMT * ((((1 + 3.5%) ^ 11) - 1) / 3.5%)*(1+3.5%)
	Each payment=	38931.35/ (((((1 + 3.5%) ^ 11) - 1) / 3.5%)*(1+3.5%))
	Each payment=	$ 2,862.19