Question

An investment offers $6,260 per year for 17 years, with the first payment occurring 11 years from now. If the required return is 3 percent, what is the value of the investment? (HINT: Remember that when you calculate the PV of the annuity, the claculator gives you the present value of the annuity 1 period before the annuity starts. So if the annuity starts in year 7, that calculator will to give you the persent value of annuity in year 6. Now you have to bring this number to period 0 by inputting: N=6 (1 period before the annuity starts, in your case it would be a different number depending when your annuity starts) R=3 FV=Present value of annuity you found in step 1. And you solve for PV)

Answer 1

Answer: $61,328.15

Explanation:

The amount paid is per year so this is an annuity. It will begin 11 years from now so one should find the present value in that year:

Present Value of annuity = Annuity * ( 1 - ( 1 + rate) ^ - no. of periods) / rate

= 6,260 * ( 1 - ( 1 + 3%) ⁻¹⁷) / 3%

= $82,419.90

That is the present value if the annuity starts 11 years from now which means that it is the present value 10 years from now (ordinary annuities are paid end of period).

You need to discount to current period:

= 82,419.90 / ( 1 + 3%)¹⁰

= $61,328.15