## Finding the Number of Payments

You ran a little short on your spring break vacation, so you put \$1,000 on your credit card. You can only afford to make the minimum payment of \$20 per month. The interest rate on the credit card is 1.5 percent per month. How long will you need to pay off the \$1,000?

What we have here is an annuity of \$20 per month at 1.5 percent per month for some unknown length of time. The present value is \$1,000 (the amount you owe today). We need to do a little algebra (or else use a financial calculator):

\$1000

(\$1,000/20) x .015 Present value factor 1.015f

\$20 X [(1 - Present value factor)/.015] 1 - Present value factor .25 = 1/(1 + r)f 1/.25 = 4

At this point, the problem boils down to asking the question, How long does it take for your money to quadruple at 1.5 percent per month? Based on our previous chapter, the answer is about 93 months:

It will take you about 93/12 = 7.75 years to pay off the \$1,000 at this rate. If you use a financial calculator for problems like this one, you should be aware that some automatically round up to the next whole period.

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