Question

Kevin Winthrop is saving for an Australian vacation in three years. He estimates that he will need $4,880 to cover his airfare and all other expenses for a week-long holiday in Australia. If he can invest his money in an S&P 500 equity index fund that is expected to earn an average annual return of 9.1 percent over the next three years, how much will he have to save every year if he starts saving at the end of this year?

Answer 1

FV of annuity
The formula for the future value of an ordinary annuity, as opposed to an annuity due, is as follows:
P = PMT x ((((1 + r) ^ n) - 1) / i)
Where:
P = the future value of an annuity stream
PMT = the dollar amount of each annuity payment
r = the effective interest rate (also known as the discount rate)
i=nominal Interest rate
n = the number of periods in which payments will be made
Interest	9%
Annual Payment	PMT
Time in years	3
4880	P = PMT x ((((1 + r) ^ n) - 1) / i)
4880	=PMT * ((((1 + 9.1%) ^ 3) - 1) / 9.1%)
4880	=PMT * 3.281281
PMT=	4880/3.281281
PMT=	1,487.22