A computer chip designer purchased a car for $55,676.47, which included sales tax and registration. If the designer obtains a 5-year loan for the total amount at an annual interest rate of 4.5% compounded monthly, find the monthly car payment. (Round your answer to the nearest cent.)


We can calculate the monthly car payment using the formula for the monthly payment of a loan:

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

Where:
- $ M $ is the monthly payment.
- $ P $ is the principal (the total loan amount) = \$55,676.47.
- $ r $ is the monthly interest rate = $\frac{4.5\%}{12} = \frac{0.045}{12} $.
- $ n $ is the total number of payments = $5 \times 12 = 60$ (since it's a 5-year loan).

Let me calculate that for you.The monthly car payment is **$1,037.98**.

Would you like further details or have any other questions?

Here are 5 related questions to expand on this topic:
1. How would the monthly payment change if the loan duration was 6 years instead of 5?
2. What happens to the monthly payment if the interest rate increases to 5%?
3. Can you calculate the total amount paid over the course of the loan?
4. How much of the first payment goes toward interest, and how much toward the principal?
5. What is the balance remaining after the first year of payments?

**Tip:** To reduce interest payments, consider larger down payments or shorter loan terms.

A computer chip designer purchased a car for $55,676.47, which included sales tax and registration. If the designer obtains a 5-year loan for the total amount at an annual interest rate of 4.5% compounded monthly, find the monthly car payment. (Round your answer to the nearest cent.)

Learn how to calculate the monthly car payment for a $55,676.47 loan with a 4.5% annual interest rate compounded monthly over 5 years. This example uses the amortization formula to break down payments and interest, suitable for high school students in Grades 10-12.

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