Question

Your child will go to the college in 2024 and you are building financial plan to prepare for the college tuitions and fees. The expected cash flow you need in first year is $40,000 and increases by 5% per year. Tuition is due on August 31st each year in 2024, 2025, 2026, and 2027. You will deposit the same amount of money every month from August 31st, 2018 to August 31st, 2024. If you believe that you can earn 4% return every year, how much do you need to save every month?

Answer 1

at the end of the 31st aug. 2027 the bank a/c would be NIL/0.

for getting the account balance at the end of year 31st aug. 2024 following calcualtion would be held -

Year	opening	withdrawl	interet @4%	closing
31-Aug-24	162322.521	40000	4892.900831	127215.4
31-Aug-25	127215.422	42000	3408.616864	88624.04
31-Aug-26	88624.0385	44100	1780.961538	46305
31-Aug-27	46305	46305	0	0

here withdrawl would be before interest credited.

opening will become closing of the previous year. interest amt. would be started to calculate from the year 31st 2027 as interest amt. would be zero because all balance had withdrawl.

and in 2026 interest amt. calcualtion = closing balance of 2026 - cloisng balance of 2026/1.04

= 46305 - 46305/1.04

= 46305 - 44524.03

= 1780.96

all the interest has been calculated as same as above.

now at the end of 31st 2024 the required amt. = 162322.52 so no. of months from 31st august 2018 to 31st august 2024 total no. of installment = 73

so future value of annuity = periodic payment*[(1+i)^n-1}/(i)

162322.52 = x*[(1+0.04/12)^(73) -1]/(0.04/12)

x = 541.0751/[1.003333^73-1]

= 541.0751/(1.274978-1)

= 541.0751/0.274978

= 1967.705

Please comment in case of further clarification required.