James Street\'s son, Harold, is 10 years old today. Harold is already making pla
ID: 2708997 • Letter: J
Question
James Street's son, Harold, is 10 years old today. Harold is already making plans to go to college on his 18th birthday, and his father wants to start putting money away now for that purpose. Street estimates that Harold will need $18,000, $19,000, $20,000, and $21,000 to pay for his freshman, sophomore, junior, and senior years, respectively. He plans to make these amounts available to Harold at the beginning of each of these years.
Street would like to make eight annual deposits (the first of which would be made on Harold's 11th birthday, 1 year from now, and the last on his 18th birthday, the day he leaves for college) in an account earning 10% annually. He wants the account to eventually be worth enough to just pay for Harold's college expenses. Any balance remaining in the account will continue to earn the 10%. How much will Street have to deposit in this planning account each year to provide for Harold's education?
Explanation / Answer
Calculation of deposit in planning account each year to provide for Harold's education:
Value of fees at the end of year 18 (8 years from now):
Year end
Fees (CF)
PVF (10%)
PV = CF*PVF
0
$ 18,000.00
1
$ 18,000.00
1
$ 19,000.00
0.909091
$ 17,272.73
2
$ 20,000.00
0.826446
$ 16,528.93
3
$ 21,000.00
0.751315
$ 15,777.61
Value of fees at the end of year 18 (8 years from now)
$ 67,579.26
Future value of annuity $ 1 (8 years , 10%)
11.43589
Deposit in planning account each year = 67579.26 / 11.43589
$ 5,909.40
Calculation of deposit in planning account each year to provide for Harold's education:
Value of fees at the end of year 18 (8 years from now):
Year end
Fees (CF)
PVF (10%)
PV = CF*PVF
0
$ 18,000.00
1
$ 18,000.00
1
$ 19,000.00
0.909091
$ 17,272.73
2
$ 20,000.00
0.826446
$ 16,528.93
3
$ 21,000.00
0.751315
$ 15,777.61
Value of fees at the end of year 18 (8 years from now)
$ 67,579.26
Future value of annuity $ 1 (8 years , 10%)
11.43589
Deposit in planning account each year = 67579.26 / 11.43589
$ 5,909.40
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