Answer:
about 14 months
Explanation:
Questions regarding loan payments, values, interest amounts, number of payments, and so on, are conveniently answered by the financial formulas available in many apps, calculators, and spreadsheets. Here, we want to solve for the number of payments.
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The time-value-of-money app on a TI-84 calculator tells us the number of monthly payments is 13.98. It will take about 14 months to pay off the credit card balance.
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Alternate solutions
You can also use a graphing calculator to find the time value needed in the amortization formula that corresponds to a monthly payment amount of $300 on a loan of $3850 at 13.99% interest compounded 12 times per year. This is shown in the second attachment.
The algebraic solution is a little messy, and involves logarithms, but you can solve it that way, too.
A = P(r/n)/(1 -(1 +r/n)^(-nt))
gives the monthly payment A on a loan of principal P at annual rate r compounded n times per year for t years. We want to find the value of nt for P=3850, A=300, r=0.1399, n=12.
Putting in the numbers, we get ...
300 = 3850(0.1399/12)/(1 -(1 +0.1399/12)^(-nt))
(1.011658333...)^(-nt) = 0.8503847222... . . . . isolate nt term
nt = -log(0.8503857222...)/log(1.011658333...) ≈ 13.982213...