Annuity due: You plan to save $1,400 for the next four years, beginning now, to pay for a vacation. If you can invest it at 6 per cent, how much will you have at the end of four years? Round to the nearest dollar.

Question

Quizplus · Accepted Answer

Since this is an annuity due, we must use the formula for present value of an annuity due instead of the formula for regular present value. The formula is:

PV = PMT x [(1 + r) x ((1 + r)^n - 1) / r]

where PV is the present value, PMT is the recurring payment, r is the interest rate per period, and n is the number of periods.

Plugging in the values, we get:

PV = $1,400 x [(1 + 0.06) x ((1 + 0.06)^4 - 1) / 0.06]
PV = $5,820.98

Since we are asked for the future value, we can simply multiply this by (1 + r)^(n-1):

FV = $5,820.98 x (1 + 0.06)^3
FV = $6,491.69

Rounding to the nearest dollar gives us choice D, $6,492.

Annuity Due: You Plan to Save $1,400 for the Next