Suppose you take out a 36 -month installment loan to finance a delivery van for . The payments are per month, and the total finance charge is .
After 25 months, you decide to pay off the loan. After calculating the finance charge rebate, find your loan payoff (in ). (Round your answer to the nearest cent.)

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Ask by Bright Ayala. in the United States

Mar 26,2025

Question

Suppose you take out a 36 -month installment loan to finance a delivery van for . The payments are per month, and the total finance charge is .
After 25 months, you decide to pay off the loan. After calculating the finance charge rebate, find your loan payoff (in ). (Round your answer to the nearest cent.)

Need Help? Read It Watch il Master II

Ask by Bright Ayala. in the United States

Mar 26,2025

UpStudy AI · Accepted Answer

We start with some key details:
- Loan amount: $$ \$26{,}100 $$
- Total number of months: $$ 36 $$
- Monthly payment: $$ \$987 $$
- Total finance (interest) charge over 36 months: $$ \$9{,}432 $$

If you were to pay the full term, your total payments would be:
$$
36 \times 987 = \$35{,}532
$$
and indeed,
$$
\$35{,}532 - \$26{,}100 = \$9{,}432.
$$

Because you decide to pay off the loan after 25 months, you are not using the full 36 months. Therefore, part of the finance charge has not been “earned” by the lender. This unearned portion is called the finance charge rebate.

**Step 1. Calculate the amount of interest “earned” in 25 months.**

Since the finance charge is spread evenly over 36 months, the interest earned by the lender in 25 months is:
$$
\text{Earned Interest} = \frac{25}{36} \times 9{,}432.
$$
Notice that:
$$
\frac{9{,}432}{36} = 262,
$$
so
$$
\text{Earned Interest} = 25 \times 262 = 6{,}550.
$$

**Step 2. Calculate the unearned (rebate) portion of the finance charge.**

The unearned finance charge is the total finance charge minus the interest earned in 25 months:
$$
\text{Unearned Finance Charge} = 9{,}432 - 6{,}550 = 2{,}882.
$$

**Step 3. Determine the remaining scheduled payments if you had kept the loan.**

After 25 months, there are:
$$
36 - 25 = 11 \text{ months}
$$
of payments remaining. The total of these remaining payments is:
$$
11 \times 987 = 10{,}857.
$$

**Step 4. Compute the loan payoff amount.**

Because you are paying off early, you only owe the remaining principal. The remaining principal is the total of the remaining scheduled payments minus the unearned finance charge (which the lender has not “earned” yet). Thus:
$$
\text{Loan Payoff} = 10{,}857 - 2{,}882 = 7{,}975.
$$

Therefore, the loan payoff amount is:
$$
\$7{,}975.00.
$$
The loan payoff amount is \$7,975.00.

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