You wish to finance the purchase of a boat home for $$ \$ 38,600 $$. A finance company offers an APR of $$ 10 \% $$ on a 24-month installment loan. After first using Table 13-1 to find the finance charge, calculate the monthly payment. Select one: O. $$ \$ 1,781.23 $$ O b. $$ \$ 1,619.08 $$ oc. $$ \$ 1,769.17 $$ o d. $$ \$ 1,608.33 $$

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UpStudy AI · Accepted Answer

We begin by noting that the finance company is offering a 24‐month installment loan at an APR of $$10\%$$. Although Table 13–1 (which we assume gives a factor or finance charge amount for various loan terms and interest rates) is used to first compute the finance charge, we can solve for the monthly payment directly by using the standard annuity (installment loan) formula.

Let

- $$ P = \$38,\!600 $$ (the amount financed),
- $$ n = 24 $$ (the number of months), and
- $$ i = \frac{10\%}{12} = \frac{0.10}{12} \approx 0.0083333 $$ (the monthly interest rate).

The monthly payment $$ M $$ is given by the formula

$$
M = P \cdot \frac{i(1+i)^n}{(1+i)^n - 1}.
$$

Substitute the known values:

$$
M = 38600 \cdot \frac{0.0083333 \, (1.0083333)^{24}}{(1.0083333)^{24} - 1}.
$$

Step 1. Compute $$(1+i)^n$$:

$$
(1.0083333)^{24} \approx 1.220.
$$

Step 2. Compute the numerator:

$$
0.0083333 \times 1.220 \approx 0.0101667.
$$

Step 3. Compute the denominator:

$$
1.220 - 1 = 0.220.
$$

Step 4. Compute the factor:

$$
\frac{0.0101667}{0.220} \approx 0.04621.
$$

Step 5. Finally, compute the monthly payment:

$$
M \approx 38600 \times 0.04621 \approx 1781.23.
$$

Thus, the monthly payment is approximately $$\$1,\!781.23$$.

The correct answer is:

$$
\boxed{\$1,\!781.23}
$$
The monthly payment is approximately \$1,781.23.

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