Suppose $250,000 is used to establish an annuity that earns 6%, compounded quarterly, and pays $6000 at the end of each quarter. It will take about 120 quarters until the account balance reaches $0.
Amount invested (Present value) = $250000
Quarterly payment (At the end of each quarter) (P) = $4500
Interest Rate (Quarterly) (r) = 6% /4
= 1.5% = 0.015
A number of quarters (n) = ?
Future value at the end = 0
Present value of Annuity formula:
Present value = P × [tex](1-(1+r))^{(-n)} / r[/tex]
250000 = 4500 × [tex](1-((1+0.015))^{(-n)} / 0.015[/tex]
250000 = 300000 × [tex](1-((1+0.015)}}^{(-n)}[/tex]
250000 / 300000 = [tex]1-(1+0.015)^{(-n)}[/tex]
0.83333 = [tex]1-(1.015)^{(-n)[/tex]
n = 120
Hence is shall take 120 Quarters until the account balance is $0.
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