# math

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Tyler buys a stereo system for \$1200, and pays for it using a credit card. This particular card charges 1.5 percent monthly interest on the unpaid balance, and requires a minimum payment of \$20 each month. Suppose that Tyler pays only the minimum amount each month. How long will it take Tyler to pay off the debt in this way, and how much will the bank eventually receive for its \$1200 loan to Tyler?

• math -

1200 = 20(1 - 1.015^-n)/.015
0.9 = 1-1.015^-n
1.015^-n = 0.1
log (1.015^-n) = log 0.1
-n = log 0.1 / log 1.015 = -154.65
n = appr 155 months

Seems harsh, but that is reality.
Considering that the interest in the first month is \$18, he pays back only about \$2 a month for quite some time
e.g.
2nd month:
Balance = 1198.00
interest = 17.97
repayment = \$2.03

3rd month:
Balance = 1198.97
interest = 17.94
repayment = \$2.06

4th month:
Balance = 1193.91
interest = 17.91
repayment = \$2.09

etc.

notice that the repayment increases only by about 3 cents per month for quite a while.

• math -

Thanks, how much money will the bank receive at the end of the 13 years?

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