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

28 month (approx)

Step-by-step explanation:

Given

Present value = $470

Monthly Payment = $20

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

=0.0125

`Present Value = PMT [(1-(1+i)^(-n))/(i)] \\470 = 20 [(1-(1+0.0125)^(-n))/(0.0125)]\\470/20 = [(1-(1+0.0125)^(-n))/(0.0125)]\\23.5 * 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= (1)/((1.0125)^(n))\\(1.0125)^(n)=1.4159292\\n=28(approx)`