A logo design company purchases four new computers for $17,500. The company finances the cost of the computers for 3 years at an annual interest rate of 6.125% compounded monthly. Find the monthly payment (in dollars) for this loan.

We can calculate the monthly payment for the loan using the formula for the monthly payment on a loan with compound interest:

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

Where:
- $ M $ is the monthly payment.
- $ P $ is the principal amount (the total loan amount).
- $ r $ is the monthly interest rate (annual interest rate divided by 12).
- $ n $ is the total number of payments (number of months over the loan period).

### Given:
- Principal $ P = 17,500 $
- Annual interest rate $ = 6.125\% $
- Loan period = 3 years (36 months)

Now, let's calculate the monthly payment:

1. **Monthly interest rate** $ r $:
\[
r = \frac{6.125\%}{12} = \frac{0.06125}{12} = 0.005104167
\]

2. **Total number of payments** $ n $:
\[
n = 3 \text{ years} \times 12 \text{ months/year} = 36 \text{ months}
\]

Now, let's compute the monthly payment using the formula.The monthly payment for the loan is approximately **$533.38**.

Would you like more details, or do you have any other questions?

Here are five related questions to explore:
1. How does changing the interest rate affect the monthly payment?
2. What would the payment be if the loan period was extended to 5 years?
3. How much total interest will the company pay over the loan period?
4. What would happen if the loan was compounded annually instead of monthly?
5. How would a down payment on the computers affect the loan calculations?

**Tip:** Paying off loans faster by making additional payments can significantly reduce the total interest paid.

A logo design company purchases four new computers for $17,500. The company finances the cost of the computers for 3 years at an annual interest rate of 6.125% compounded monthly. Find the monthly payment (in dollars) for this loan.

Calculate the monthly payment for a $17,500 loan over 3 years with an annual interest rate of 6.125%, compounded monthly. Learn how to apply the loan amortization formula to solve real-world problems, including calculating interest and principal payments. Suitable for Grades 10-12 students.

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