Question

Like many college students, Daphne applied for and got a credit card that has an annual percentage rate (APR) of 15%. The first thing she did was buy a new DVD player for $400. At the end of the month, her credit card statement said she only needed to make a minimum monthly payment of $15. Assume Daphne makes her payment when she sees her statement at the end of each month. If Daphne doesn't charge anything else and only makes the minimum monthly payments, approximately how many months would it take her to completely pay off the DVD player

Answer 1

Answer:

approximately 32.64 months ≈ which we can round to 33 months

Explanation:

assuming that Daphne only pays the minimum payment, the balance on her credit will decrease only a small bit per month.

We can use the present value of an annuity formula:

present value = monthly payment x  [1 - 1/(1 + i)ⁿ ] / i

present value = $400

monthly payment = $15

i = 15% / 12 = 1.25% = 0.0125

400 = 15 x [1 - 1/(1 + 0.0125)ⁿ ] / 0.0125

400 = 15/0.0125 x [1 - 1/(1 + 0.0125)ⁿ ]

400 = 1,200 x [1 - 1/(1 + 0.0125)ⁿ ]

400 / 1,200 = [1 - 1/(1 + 0.0125)ⁿ ]

1/3 = 1 - 1/(1 + 0.0125)ⁿ

1/(1 + 0.0125)ⁿ = 2/3

1 = 2/3 x (1 + 0.0125)ⁿ

1.5 = (1 + 0.0125)ⁿ

1.5 = 1.0125ⁿ

n = log 1.5 / log 1.0125 = 32.64 months