Question

How many months will it take to pay off a $470 debt, with monthly payments of $20 at the end of each month, if the annual interest rate is 15%, compounded monthly?

Answer 1

Answer:

28 month (approx)

Explanation:

Given

Present value = $470

Monthly Payment = $20

Interest Rate = 15% annual = 15% / 12 = 1.25% monthly

                                                             =0.0125

$Present Value = PMT [\frac{1-(1+i)^{-n}}{i}] \\470 = 20 [\frac{1-(1+0.0125)^{-n}}{0.0125}]\\470/20 = [\frac{1-(1+0.0125)^{-n}}{0.0125}]\\23.5 \times 0.0125 =1-(1+0.0125)^{-n}\\1-0.29375= (1+0.0125)^{-n}\\0.70625 = (1+0.0125)^{-n}\\0.70625 =(1.0125)^{-n}\\0.70625= \frac{1}{(1.0125)^{n}}\\(1.0125)^{n}=1.4159292\\n=28(approx)$