You have \( \$ 4,000 \) on a credit card that charges a \( 23 \% \) interest rate. If you want to pay off the credit card in 5 years, how much will you need to pay each month (assuming you don't charge anything new to the card)? \( \$ \) each month Enter anintererordeamal numbermore.

We start by using the formula for the payment on an amortized loan: \[ \text{PMT} = P \cdot \frac{r(1+r)^n}{(1+r)^n-1} \] where - \(P = 4000\) is the principal, - \(r\) is the monthly interest rate, and - \(n\) is the total number of payments. Since the annual interest rate is \(23\%\), the monthly interest rate is \[ r = \frac{0.23}{12} \approx 0.01916667. \] For a 5‑year period with monthly payments, the number of payments is \[ n = 5 \times 12 = 60. \] Substitute these values into the formula: \[ \text{PMT} = 4000 \cdot \frac{0.01916667 \, (1+0.01916667)^{60}}{(1+0.01916667)^{60}-1}. \] First, calculate \((1+r)^{60}\): \[ (1+0.01916667)^{60}. \] Using an approximation (via the logarithm method or a calculator) we find: \[ (1+0.01916667)^{60} \approx 3.123. \] Now, compute the numerator: \[ r(1+r)^n \approx 0.01916667 \times 3.123 \approx 0.05984. \] Then, the denominator is: \[ (1+r)^n-1 \approx 3.123-1 = 2.123. \] So the fraction becomes: \[ \frac{0.05984}{2.123} \approx 0.02818. \] Finally, the monthly payment is: \[ \text{PMT} \approx 4000 \times 0.02818 \approx 112.72. \] Thus, you would need to pay about \(\$112.72\) each month.