Your credit card has a balance of \( \$ 4900 \) and an annual interest rate of \( 17 \% \). You decide to pay off the balance over four years. If there are no further purchases charged to the card, you must pay \( \$ 141.37 \) each month, and you will pay a total interest of \( \$ 1885.76 \). Assume you decide to pay off the balance over one year rather than four. How much more must you pay each month and how much less will you pay in total interest? Use PMT \( =\frac{P\left(\frac{r}{n}\right)}{1-\left(1+\frac{r}{n}\right)^{-n t}} \) to determine the regular payment amount. You will pay \( \$ 305.51 \) more each month. (Round to the nearest cent as needed.) You will pay \( \$ \square \) less in total interest. (Round to the nearest cent as needed.)

We begin with the payment formula for an amortized loan \[ \text{PMT} = \frac{P\left(\frac{r}{n}\right)}{1-\left(1+\frac{r}{n}\right)^{-n t}}, \] where - \( P = 4900 \) is the principal, - \( r = 0.17 \) is the annual interest rate, - \( n = 12 \) is the number of payments per year, - \( t \) is the number of years. For the four‐year payoff, the monthly payment is given as \[ \text{PMT}_{4\text{yr}} = 141.37. \] We wish to compare this to the one‐year payoff. In the one‐year case we set \( t = 1 \) so that \[ \text{PMT}_{1\text{yr}} = \frac{4900\left(\frac{0.17}{12}\right)}{1-\left(1+\frac{0.17}{12}\right)^{-12}}. \] A calculator (or equivalent computation) gives approximately \[ \text{PMT}_{1\text{yr}} \approx 446.88. \] Thus, the additional amount you must pay each month when shortening the term is \[ 446.88 - 141.37 = 305.51. \] Next, we calculate the total interest paid in the one‐year option. The total amount paid over one year is \[ \text{Total Paid}_{1\text{yr}} = 12 \times 446.88 = 5362.56. \] Subtracting the principal, the total interest is \[ \text{Interest}_{1\text{yr}} = 5362.56 - 4900 = 462.56. \] We are told that when paying over four years the total interest is \[ \text{Interest}_{4\text{yr}} = 1885.76. \] Thus, the interest saved by paying off in one year (i.e. the reduction in total interest) is \[ 1885.76 - 462.56 = 1423.20. \] So in summary: - You will pay \(\$305.51\) more each month. - You will pay \(\$1423.20\) less in total interest.