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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.)

Respuesta :

Answer:

n = 121

Step-by-step 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 = [tex]P\times\dfrac{1-(1+r)^{-n}}{r}[/tex]

[tex]250000 = 5500\times\dfrac{1-(1+0.02)^{-n}}{0.02}[/tex]

1.02⁻ⁿ = 0.091

-n ln(1.02) = ln (0.091)

n = 121

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

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