Question

You plan to work for 40 years and then retire using a 25-year annuity. You want to arrange a retirement income of $4000 per month. You have access to an account that pays an APR of 6.0% compounded monthly. This requires a nest egg of $620,827.46.
What monthly deposits are required to achieve the desired monthly yield at retirement? (Round your answer to the nearest cent.)

Answer 1

Answer:

  $311.74

Step-by-step explanation:

A financial calculator computes the payment amount to be $311.74.

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Your graphing calculator may have the capability to do this. Certainly, such calculators are available in spreadsheet programs and on the web.

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The appropriate formula is the one for the sum of terms of a geometric series.

  Sn = a1·((1+r)^n -1)/(r) . . . . . where r is the monthly interest rate (0.005) and n is the number of payments (480). Filling in the given numbers, you have ...

  $620827.46 = a1·(1.005^480 -1)/.005 = 1991.4907·a1

Then ...

  $620827.46/1991.4907 = a1 ≈ $311.74