If a person borrows ​$14,400 and repays the loan by paying ​$300 per month to reduce the loan and 1​% of the unpaid balance each month for the use of the​ money, what is the total cost of the loan over 48 ​months?

To determine the total cost of the loan over 48 months, let's break down the payments and interest.

### Step 1: Calculate Monthly Interest Payment
The person pays 1% of the unpaid balance each month as interest. The interest decreases as the unpaid balance decreases over time.

If the unpaid balance at the start of a month is $ P $, the interest payment for that month will be:
\[
\text{Interest payment} = 0.01 \times P
\]

### Step 2: Loan Repayment Calculation
The borrower also pays $300 per month toward reducing the loan principal. After each month’s payment, the new balance will be:
\[
\text{New Balance} = P - 300
\]
The next month, the interest will be calculated on this reduced balance.

### Step 3: Create the Payment Schedule
We need to simulate this process month by month:
- In the first month, the person owes $14,400.
- The person pays $300, reducing the loan, and 1% interest on the balance for that month.
- This repeats for 48 months.

The goal is to determine the total interest paid over the course of the loan and add it to the total payments.

I will now compute the total cost of the loan over the 48 months.The total cost of the loan over 48 months is $17,928, which includes $3,528 in interest payments. This means the borrower will pay $14,400 towards reducing the loan principal and $3,528 for the use of the money (interest).

Would you like more details on any of the steps?

Here are some related questions:
1. How does the interest rate impact the total cost of a loan?
2. What would happen if the monthly payments were higher or lower?
3. How is compound interest different from this type of interest calculation?
4. What is the relationship between the loan term and total interest paid?
5. How would an increase in the interest rate affect the final total?

**Tip:** Reducing loan balances quickly can save significantly on interest over time.

Discover how to calculate the total cost of a $14,400 loan with a $300 monthly payment and 1% monthly interest on the unpaid balance. Learn step-by-step about loan amortization, interest calculation, and reducing the principal over 48 months. Suitable for high school students in Grades 9-12.

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