Compute an effective i for the time period between withdrawals.

On January 1, a woman deposits $5000 in a'credit union that pays 8% nominal annual interest, compounded quarterly. Shewishes to with draw all the money in five equal yearly sums,beginning December 31 of the first year. How much should she with draw each year?

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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