Gwen plans to retire in 3 years with $426,000 in her account, which has an annual return of 6.29 percent. If she receives annual payments of X, with her first payment of X received in 4 years and her last payment of X received in 9 years, then what is X, the amount of each payment?
| We can use the present value of annuity formula to calculate the annual payment to be received by Gwen | |||||||||
| Present Value of annuity = X * {[1 - (1+r)^-n]/r} | |||||||||
| Present value of annuity = amount in retirement account in 3 years = $426000 | |||||||||
| X = Annual payment received by Gwen = ? | |||||||||
| r = annual rate of return = 6.29% | |||||||||
| n = number of annual payments = 6 [from 4th year to 9th Year] | |||||||||
| 426000 = X * {[1 - (1+0.0629)^-6]/0.0629} | |||||||||
| 426000 = X x 4.872837 | |||||||||
| X = 87,423.40 | |||||||||
| Amount of each payment = $87,423.40 | |||||||||
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