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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

Ask by Hardy Long. in the United States
Mar 11,2025

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Answer

The monthly amortization payment is approximately \$706.10.

Solution

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. \(\$706.10\).

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To find the monthly amortization payment needed to pay off a debt of $15,000 in 2 years at a 12% interest rate compounded monthly, you can use the formula for monthly payments on an amortizing loan, which is \( M = P \times \frac{r(1+r)^n}{(1+r)^n - 1} \). Here, \( P \) is the principal ($15,000), \( r \) is the monthly interest rate (12% annual rate, or 1% monthly), and \( n \) is the total number of payments (24 months for 2 years). Plugging in the values will yield one of the provided options. The payment calculated would be approximately $706.10, making option (d) the correct answer. That means Fresh Linens would need to set aside a nice chunk of change each month to take care of that debt!

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