Question

Sasha plans to retire in 7 years with 533,117 dollars in her account, which has an annual return of 4.94 percent. If she receives payments of 86,000 dollars per year and she receives her first 86,000 dollar payment in 7 years, then how many payments of 86,000 dollars can Sasha expect to receive? Round your answer to 2 decimal places (for example, 2.89, 0.70, or 1.00).

Answer 1

We can use the present value of annuity due formula to calculate the number of payments of $86000 can Sasha expect to receive
Present value of annuity due = P + P {[1 - (1+r)^-(n-1)]/r}
Present value of annuity due = amount in retirement account in 7 years = $5,33,117
P = annual payment = $86000
r = annual return = 4.94%
n = number of annual payments = ?
533117 = 86000 + 86000 {[1 - (1+0.0494)^-(n-1)]/0.0494}
447117 = 1740890.69 x [1 - 1.0494^-(n-1)]
0.2568 = 1 - 1.0494^-(n-1)
0.7432 = 1.0494^-(n-1)
n = 7.15
Sasha expect to receive 7.15 payments of $86000 each.