Question

A eight-year growing annuity of eight annual payments will begin 6 years from now, with the first payment $6,200 coming 7 years from now and annual payment growing at 3 percent. If the annual discount rate is 7 percent, what is the value of this growing annuity 4 years from now?

Answer 1

first, we need to find the value at 6 years from now,

So,

PV of Growing Annuity at (Year=6) = [Annual Payment / (r - g)] * [1 - {(1 + g)/(1 + r)}ⁿ]

= [$6,200 / (0.07 - 0.03)] * [1 - {(1 + 0.03) / (1 + 0.07)}⁸]

= $155,000 * [1 - 0.7373]

= $155,000 * 0.2627 = $40,722.88

PV of Growing Annuity at (Year=4) = PV of Growing Annuity at (Year=6) / (1 + r)²

= $40,722.88 / (1 + 0.07)² = $40,722.88 / 1.1449 = $35,568.94