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

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UpStudy AI · Accepted Answer

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. $$\$706.10$$.
The monthly amortization payment is approximately \$706.10.

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