The owner of a construction company purchased a cement mixer truck for $180,000 and made a down payment of $45,000. The remaining balance was financed for 10 years at an annual interest rate of 7.25% compounded monthly. Find the monthly payment (in dollars). (Round your answer to the nearest cent.)

To calculate the monthly payment for the cement mixer truck, we will use the formula for the monthly payment on a loan, which is derived from the **amortization formula**:

\[
M = \frac{P \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1}
\]

Where:
- $ M $ is the monthly payment.
- $ P $ is the principal loan amount (the amount that needs to be financed).
- $ r $ is the monthly interest rate (annual interest rate divided by 12).
- $ n $ is the total number of monthly payments (loan term in years multiplied by 12).

### Given:
- The total price of the truck is \$180,000.
- A down payment of \$45,000 was made, so the remaining balance to be financed is:
  \[
  P = 180,000 - 45,000 = 135,000
  \]
- The annual interest rate is 7.25%, so the monthly interest rate is:
  \[
  r = \frac{7.25\%}{12} = \frac{0.0725}{12} = 0.00604167
  \]
- The loan term is 10 years, so the total number of payments is:
  \[
  n = 10 \times 12 = 120
  \]

Now, let's calculate the monthly payment $ M $.

The monthly payment for the cement mixer truck is **$1,584.91**.

Would you like further details or have any other questions?

Here are 5 related questions to expand on this topic:
1. What is the total interest paid over the 10-year loan period?
2. How much will the total cost of the truck be after 10 years, including interest?
3. How would the monthly payment change if the interest rate were different?
4. What happens if the loan is repaid early—how does that affect the overall cost?
5. How would the payment change with a shorter loan term, say 5 years?

**Tip:** The longer the loan term, the lower the monthly payment, but the higher the total interest paid.

Discover how to calculate the monthly payment for a cement mixer truck costing $180,000 with a $45,000 down payment, financed over 10 years at an annual interest rate of 7.25% compounded monthly. This problem covers loan amortization and compound interest, ideal for high school or college students.

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