Question

Jack and jill have just had their first child. if college is expected to cost ​$180 comma 000180,000 per year in 1818 ​years, how much should the couple begin depositing annually at the end of each year to accumulate enough funds to pay the first​ year's tuition at the beginning of the 19th​ year? assume that they can earn an annual rate of return of 66​% on their investment.

Answer 1

Given:
tuition: 180,000 per year
period to save: 18 years
annual rate of return : 6%

FV = PV * (1+r)^t
180,000 = PV * (1 + 0.06)¹⁸
180,000 = PV * (1.06)¹⁸
PV = 180,000 / (1.06)¹⁸ = 180,000 / 2.854 = 63,069.38

Jack and Jill will have to invest 63,069.38 in the first year to have a total of 180,000 after 18 years. 

Using Future Value Annuity formula:

FV of Annuity = P [{(1+r)^n - 1} / r]

180,000 = P [{(1.06)¹⁸ - 1} / 0.06]
180,000 = P (30.906)
P = 180,000 / 30.906
P = 5,824.11

Jack and Jill will have to deposit 5,824.11 every end of the year for the total to reach 180,000 after 18 years.