## How Much Can You Afford i

After carefully going over your budget, you have determined you can afford to pay \$632 per -1

month towards a new sports car. You call up your local bank and find out that the going rate is 1 percent per month for 48 months. How much can you borrow?

To determine how much you can borrow, we need to calculate the present value of \$632 per month for 48 months at 1 percent per month. The loan payments are in ordinary annuity form, so the annuity present value factor is:

Annuity PV factor = (1 - Present value factor)/r = [1 - (1/1.0148)]/.01 = (1 - .6203)/.01 = 37.9740

With this factor, we can calculate the present value of the 48 payments of \$632 each as:

Therefore, \$24,000 is what you can afford to borrow and repay.

Annuity Tables Just as there are tables for ordinary present value factors, there are tables for annuity factors as well. Table 6.1 contains a few such factors; Table A.3 in the appendix to the book contains a larger set. To find the annuity present value factor we calculated just before Example 6.5, look for the row corresponding to three periods and then find the column for 10 percent. The number you see at that intersection should be 2.4869 (rounded to four decimal places), as we calculated. Once again, try calculating a few of these factors yourself and compare your answers to the ones in the table to make sure you know how to do it. If you are using a financial calculator, just enter \$1 as the payment and calculate the present value; the result should be the annuity present value factor.

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