Question

A 10-year annuity of twenty $4,000 semiannual payments will begin 9 years from now, with the first payment coming 9.5 years from now.

a. If the discount rate is 12 percent compounded monthly, what is the value of this annuity 5 years from now?

b. What is the current value of the annuity?

Answer 1

a). PV of Annuity(9 years from now) = Periodic Payment * [{1 - (1 + r)^-n} / r]

= $4,000 * [{1 - (1 + 0.12/2)^-(10*2)} / (0.12/2)]

= $4,000 * [0.6882 / 0.06]

= $4,000 * 11.4699

= $45,879.68

PV of Annuity(5 years from now) = PV of Annuity(9 years from now) / (1 + r)ⁿ

= $45,879.68 / {1 + (0.12/2)]^(4*2)

= $45,879.68 / 1.5938

= $28,785.48

b). Pv of Annuity now = PV of Annuity(5 years from now) / (1 + r)ⁿ

= $28,785.48 / {1 + (0.12/2)]^(5*2)

= $28,785.48 / 1.7908

= $16,073.66