Question

Matilda is planning for her daughter’s university education to begin five years from today. She estimated the annual tuition to be R40 000 per year for a three-year degree.

Calculate how much Matilda must deposit today, at an interest rate of 8% per annum, compounded annually, for her daughter to be able to withdraw R40 000 per year for three years of university. (You can assume an interest rate of 8% throughout the period.

Answer 1

PV of annuity
P = PMT x (((1-(1 + r) ^- n)) / r)
Where:
P = the present value of an annuity stream	To be computed
PMT = the dollar amount of each annuity payment	$      40,000.00
r = the effective interest rate (also known as the discount rate)	8.00%
n = the number of periods in which payments will be made	3
PV of annuity=	PMT x (((1-(1 + r) ^- n)) / r)
PV of annuity=	40000* (((1-(1 + 8%) ^- 3)) / 8%)
PV of annuity=	$    103,083.88
The amount should be deposited today so that amount becomes $ 103,083.88 @ 8%
Initial deposit=	103083.88/(1+8%)^5
Initial deposit=	$           70,157