1. **State the problem:** You have a credit card balance of $2000 with an annual interest rate of 13%. You want to pay off the balance in 3 years by making equal monthly payments. We need to find the monthly payment amount. 2. **Formula used:** The monthly payment for a loan with principal $P$, monthly interest rate $r$, and number of payments $n$ is given by the amortization formula: $$ M = P \times \frac{r(1+r)^n}{(1+r)^n - 1} $$ where: - $M$ is the monthly payment, - $P = 2000$ is the principal, - $r = \frac{0.13}{12}$ is the monthly interest rate (annual rate divided by 12), - $n = 3 \times 12 = 36$ is the total number of monthly payments. 3. **Calculate monthly interest rate:** $$ r = \frac{0.13}{12} = 0.0108333... $$ 4. **Calculate $(1+r)^n$:** $$ (1 + 0.0108333)^{36} = (1.0108333)^{36} \approx 1.448 \text{ (rounded)} $$ 5. **Calculate numerator and denominator:** Numerator: $$ r \times (1+r)^n = 0.0108333 \times 1.448 = 0.01569 $$ Denominator: $$ (1+r)^n - 1 = 1.448 - 1 = 0.448 $$ 6. **Calculate monthly payment $M$:** $$ M = 2000 \times \frac{0.01569}{0.448} = 2000 \times 0.035 \approx 70.00 $$ 7. **Interpretation:** You need to pay approximately $70.00 each month for 3 years to pay off the $2000 balance at 13% annual interest. **Final answer:** $$ \boxed{70.00} $$