Question

Today, you borrowed $9,800 on your credit card to purchase some furniture. The interest rate is 12.6 percent, compounded monthlyHow long will it take you to pay off this debt assuming that you do not charge anything else and make regular monthly payments of $130?

Answer 1

The time period is computed as follows:

Present value = Monthly payment x [ (1 – 1 / (1 + r)ⁿ) / r ]

r will be as follows:

= 12.6% / 12 (Since the interest is compounded monthly, hence divided by 12)

= 1.05%

$ 9,800 = $ 130 x [ (1 - 1 / (1 + 0.0105) ^{n x 12} ) / 0.0105 ]

$ 9,800 / $ 130 = [ (1 - 1 / (1 + 0.0105) ^{n x 12} ) / 0.0105 ]

75.38461538 x 0.0105 = 1 - 1 / (1 + 0.0105) ^{n x 12}

0.791538462 = 1 - 1 / (1 + 0.0105) ^{n x 12}

1 / (1 + 0.0105) ^{n x 12} = 1 - 0.791538462

1 / (1 + 0.0105) ^{n x 12} = 0.208461538

1 /  0.208461538 = 1.0105 ^{12 n}

4.79704797 = 1.0105 ^{12 n}

Take log both sides, we shall get:

log 4.79704797 = 12 n x log 1.0105

1.568000722 = 12 n x 0.010445258

12 n = 1.568000722 / 0.010445258

12 n = 150.1160376

n = 150.1160376 / 12

n = 12.51 years or 150.12 months Approximately

Do ask in case of any doubts.