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.

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.