Given:

• Loan amount (principal) $P = 4700$ dollars
• Fixed APR $r = 6.5\%$ or $0.065$ as a decimal
• Loan term $n = 4$ years
• Monthly payments over $4 \times 12 = 48$ months

Let's derive the equations for each question.

1. Monthly Payment on a 4-Year Loan

To calculate the monthly payment, we can use the formula for an installment loan, which is: $M = \frac{P \cdot \frac{r}{12}}{1 - \left(1 + \frac{r}{12}\right)^{-n \cdot 12}}$ where:

• $M$ is the monthly payment,
• $P$ is the loan principal,
• $r$ is the annual interest rate (as a decimal),
• $n$ is the loan term in years.

So, in our case: $M = \frac{4700 \cdot \frac{0.065}{12}}{1 - \left(1 + \frac{0.065}{12}\right)^{-48}}$

2. Total Amount Paid Over 4 Years

The total amount paid over the 4-year period is the monthly payment multiplied by the number of months: $\text{Total Payment} = M \times (n \cdot 12)$ After calculating $M$, we can substitute it here: $\text{Total Payment} = M \times 48$

3. Total Interest Paid

The total interest paid is the total payment minus the initial loan amount: $\text{Total Interest} = \text{Total Payment} - P$ or equivalently: $\text{Total Interest} = (M \times 48) - 4700$

These three equations provide answers for each of the questions based on the loan details given.

Would you like further clarification on any of these steps?

5 Related Questions

1. What would the monthly payment be if the loan term were extended to 5 years?
2. How would a change in APR to 7.5% affect the monthly payments?
3. What portion of the monthly payment goes to interest vs. principal at the start of the loan term?
4. How much would you save on total interest if you paid off the loan in 3 years instead of 4?
5. How would the total interest paid change if you made an extra payment each year?

Tip

Always double-check that the loan's APR is converted to a decimal when inserting it into formulas for accurate calculations.