Question

A personal account earmarked as a retirement supplement contains $292,300. Suppose $250,000 is used to establish an annuity that earns 8%, compounded quarterly, and pays $5500 at the end of each quarter. How long will it be until the account balance is $0? (Round your answer UP to the nearest quarter.)

Answer 1

n = 121

Explanation:

Given,

Amount invested = $250,000

Quarterly payment (P) = $5500

Interest Rate (Quarterly) (r) = 8% /4 = 2%

Account balance = $ 0

Present value of Annuity formula ,

Present value =
`P*(1-(1+r)^(-n))/(r)`

`250000 = 5500*(1-(1+0.02)^(-n))/(0.02)`

1.02⁻ⁿ = 0.091

-n ln(1.02) = ln (0.091)

n = 121

Hence it will take 121 Quarters to account balance $0.