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Deryl wishes to save money to provide for his retirement. beginning one month from now, he will deposit a fixed amount into a retirement savings account that will earn 12% compounded monthly. he will make 360 such deposits. then, one year after making his final deposit, he will withdraw $100,000 annually for 25 years. the account balance will reduce to zero when the last withdrawal was made. the fund will continue to earn 12.68% compounded annually during these last 25 years. how much should his monthly deposits be?

Respuesta :

sqdancefan

Answer:

  $214.24

Step-by-step explanation:

The amount required to support annual payments of $100,000 for 25 years can be computed using the amortization formula:

  A = Pr/(1 -(1+r)^-t) . . . . where A is the annual payment, P is the initial principal amount, r is the annual interest rate and t is the number of years.

Filling in the numbers, we can find P to be ...

  P = A(1 -(1 +r)^-t)/r = 100,000(1 -1.1268^-25)/.1268 ≈ 748,767.70

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This we want to be the future value (S) of the series of 360 monthly payments (P) earning annual rate r. The sum of those payments is ...

  S = P((1+r/12)^360 -1)/(r/12)

Filling in the numbers and solving for P, we get ...

  748767.70 = P((1.01^360 -1)/0.01) = 3494.96413P

  P = 748767.70/3494.96413 ≈ 214.24

Deryl should deposit $214.24 monthly.

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