Question

Chlo is planning for her 15 year-old daughter’s university education.  She estimates that 1 year of university would cost $15,000 in today’s dollars, but will rise with the rate of inflation of 2% year over year.  How much would Chlo need to have accumulated by the time her daughter starts university at the age of 19 provided she attends university for 3 years and will receive funds at the beginning of each year?  Assume an investment rate of 3.6%, compounded monthly

Answer 1

The daugher is 15 year old and she will go to univeristy at 19. So the time gap is 4 year and inflation should be adjusted.

We know Future Value = Present Value(1+r)t where, r = rate and t = time

Future Value of the amount required in the beginning of the 1st year of university = 15000*(1+0.02)⁴ = $16,236.48

Future Value of the amount required in the beginning of the 2nd year of university = 15000*(1+0.02)⁵ = $16,561.21

Future Value of the amount required in the beginning of the 3rd year of university = 15000*(1+0.02)⁶ = $16,892.44

Total amount required for the education purposes = 16,236.48 + 16,561.21 + 16,892.44 = 49,690.13

Required by the question :

What amount in the beginning of the 1st year of university is needed so that the amount is compounded monthly at the rate of 3.6% and we have amount available for each year to be withdraw

Interest Rate(3.6%/12)	0.003
Total Time Period between 0 to 1	12
Total time period between payment 0 to 2	24
Year(Beginning)	0	1	2
Cash Flows	16,236.48	16,561.21	16,892.44
Present Value Factor	1/(1+r)^t	PVF at r = 0.003, t = 12	PVF at r = 0.003, t = 24
PVF	1	0.96	0.93
Present Value(as when daugher is 19)	16236.48	15976.47146	15720.63167
Amount Required(Sume of PVs)	47933.58313

So, amount required in the beginning of the university education is $47,933.58313.

For confirmation, if the amount is right, I have made a table for you aswell using excel.

Initial Amount	$47,933.58
Withdrawn in 1st year beginning	$16,236.48
Amount left for compounding	$31,697.10
Compounding on 31,697.10 for 12 months at rate monthly rate 0.003	$32,857.22	Use FV function
Amount withdrawn in 2nd year beginning	$16,561.21
Amount left for compounding	$16,296.01
Compounding on 16,296 for last 12 months at monthly rate 0.003	$16,892.44
Amount withdrawn in the beginning of the 3rd year	$16,892.44
Amount left	$0.00

If you have any doubt, ask me in the comment section.