PVoa = PMT[(1 - (1 / (1 +r)^n)) / r]
= 40,000[(1 - (1 / 1.0775^25)) / 0.0775]
= 40,000[(1 - (1 / 6.46297)) / 0.0775]
= 40k[(1 - 0.15473) / 0.0775]
= 40k[10.90674]
= $436,269.58
Amount you need to invest annually, assuming you invest for 60 - 20 = 40 years
FVoa = PMT [((1 + i)^n - 1) / i]
436,269.58 = PMT[(1.0775^20) - 1) / 0.0775]
436,269.58 = PMT[3.44985 / 0.0775]
436,269.58 = PMT[44.51422]
PMT = 436,269.58 / 44.51422]
PMT= $9,800.67883, round to $9,800.68
see bankrate.com
To supplement your retirement income, you would like to receive an additional 40000 per year for 25 years ( with the first payment at the end of the year when you're 60). You open an investment account when you are 20 years old. If the account yields 7.75% annually( and will continue to yield 7.75% through your retirement)
