### Compute an effective i for the time period between withdrawals.

SOLUTION

Since the 8% nominal annual interest rate r is compounded quarterly, we know that the effective interest rate per interest period, i, is 2%; and there are a total of 4 x 5 = 20 interest periods in 5 years. For the equation A = P (A j P, i, n) to be used, there must be as many periodic withdrawals as there'are interest periods, n. In this examplewe have 5 withdrawals and 20 interest periods.

To solve the problem, we must adjust it so that it is in one of the standard forms for which we have compound interest factors.

**Compute an effective i for the time period between withdrawals.**

Between withdrawals,W, there are four interest periods, hence m = 4 compounding subperiods per year.Since the nominal interest rate per year, r, is 8%,we canproceedto compute the effective interest rate per year.

Now the problemmay be redrawn as follows:

This diagram may be directly solved to determine the annual withdrawal W using the capital recovery factor:

The depositor should withdraw $1260 per year.

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