Fresh Linens wishes to pay off a debt of \( \$ 15,000 \) in 2 years. What amortization payment would they need to make every month, at \( 12 \% \) interest compounded monthly? (Use Table \( 12-2 \). ) Select one: a. \( \$ 625.00 \) b. \( \$ 664.81 \) c. \( \$ 684.10 \) d. \( \$ 706.10 \) Clear my choice

The amortization payment is given by the formula \[ P = L\frac{r(1+r)^n}{(1+r)^n-1} \] where: - \( L \) is the loan amount (\$15,000), - \( r \) is the periodic interest rate (monthly rate), - \( n \) is the total number of payments. Since the annual interest rate is \( 12\% \) compounded monthly, the monthly rate is \[ r = \frac{12\%}{12} = 0.01. \] There are 2 years of payments, so the total number of monthly payments is \[ n = 2 \times 12 = 24. \] Substitute these values into the formula: \[ P = 15000 \times \frac{0.01 \times (1.01)^{24}}{(1.01)^{24} - 1}. \] We first calculate \((1.01)^{24}\). Using a calculator or logarithm approximations, \[ (1.01)^{24} \approx 1.2697. \] Now plug this back into the equation: \[ P \approx 15000 \times \frac{0.01 \times 1.2697}{1.2697 - 1}. \] Calculate the numerator: \[ 0.01 \times 1.2697 = 0.012697. \] Calculate the denominator: \[ 1.2697 - 1 = 0.2697. \] Thus, \[ P \approx 15000 \times \frac{0.012697}{0.2697} \approx 15000 \times 0.04708 \approx 706.10. \] Therefore, the required monthly payment is approximately \(\$706.10\), which corresponds to choice: d. \(\$706.10\).