Question

Your daughter just turned 4 years old. You anticipate she will start University when she turns 18. You would like to have funds in a registered education savings plan (RESP) to fund her education at that time. You anticipate she will spend 6 years in university, and it will cost $20,000 per year. She will need the $20,000 at the start of each school year. When she graduates (debt free) you would also like her to have $40,000 for a down payment on a condo or to travel. If the account promises to pay a fixed interest rate (APR) of 6% per year with monthly compounding, how much money do you have to deposit each quarter to ensure you will have enough when she starts university? Assume you will make the same deposit at the end of each quarter until she starts university.

Answer 1

1. Calculate the Present value of Fees required at when she turns 18.

for this purpose we need effective annual rate and given rate is nominal rate 6% monthly compunding.

Monthly rate 6/12= 0.5%

EAR = (1+r)ⁿ -1

= (1.005)¹² -1

= 6.1678%

Amount required i.e. PV is

Year	Fees required	PV fator @ 6.1678%	Present Value
0	20000	1	20000
1	20000	0.941905173	18838.10346
2	20000	0.887185354	17743.70709
3	20000	0.835644475	16712.88949
4	20000	0.787097853	15741.95706
5	20000	0.741371539	14827.43079
6	40000	0.698301688	27932.06751
		PV	131796.1554

2. Calulate the amount need to invest per quarter from daughter Age 4 to 18.

SO we have 14 years x 4 = 56, You need Quarterly rate for that [(1.005)³ -1] = 1.5075%

Quarterly payment x cumulaive annuity fator @1.5075% for 56 years = 131796.1554

Since the calculation is big we go with financial calculator

Put values in texas ba 2 as N=56, I/Y=1.5075, PV=0, FV = 131796.1554 compute PMT = 1514.92 Approx

1514.92 Approx Qtry Needed to deposit.