Thom owes $5,000 on his credit card. The credit card carries an APR of 17.3 percent compounded monthly. If Thom makes monthly payments of $170 per month, how long will it take for him to pay off the credit card assuming that he makes no additional charges

39 months

Explanation:

loan balance $5,000

APR = 17.3% compounded monthly / 12 = 1.44167% monthly interest rate

monthly payment = $170

if we use the present value of annuity formula:

PV = payment x ({1 - [1/(1 + r)ⁿ]} / r)

5,000 = 170 x ({1 - [1/(1 + 0.0144167)ⁿ]} / 0.0144167)

29.4118 = {1 - [1/(1.0144167)ⁿ]} / 0.0144167

0.42402 = 1 - [1/(1.0144167)ⁿ

1/(1.0144167)ⁿ = 0.57598

1.0144167ⁿ = 1 / 0.57598 = 1.73617

n log1.0144167 = log1.73617

n 0.00621639 = 0.2395926

n = 0.2395926 / 0.00621639 = 38.54 ≈ since the payments must be made in full months, we have to round up to 39 months

to check our

PV = payment x ({1 - [1/(1 + r)ⁿ]} / r)

PV = 170 x ({1 - [1/(1 + 0.0144167)³⁹]} / 0.0144167)

PV = $5,044.36

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