What is the annual interest rate on twenty-year $52300 car loan that is compounded
quarterly and has monthly payments of $283.61?

Use the TVM Solver.

6.91 percent sign
blank 2.76 percent sign
4.52 percent sign
9.81 percent sign

To determine the annual interest rate on a twenty-year car loan of $52,300 with monthly payments of $283.61, compounded quarterly, we will use the Time Value of Money (TVM) Solver. Here's the step-by-step process:

1. **Identify the variables:**
   - **PV (Present Value)**: $52,300 (since it's a loan, this amount is positive as it's received now)
   - **PMT (Payment per period)**: -$283.61 (since it's a payment, this amount is negative as it's paid out)
   - **FV (Future Value)**: $0 (assuming the loan is paid off completely at the end)
   - **n (Number of periods)**: 20 years × 12 months/year = 240 months
   - **P/Y (Payments per year)**: 12
   - **C/Y (Compounding periods per year)**: 4 (quarterly)

2. **Setup the TVM Solver:**
   - PV = 52,300
   - PMT = -283.61
   - FV = 0
   - n = 240
   - P/Y = 12
   - C/Y = 4

3. **Solve for I/Y (Annual interest rate):**

Using a financial calculator or a TVM Solver app, input the above values and solve for I/Y. If using a financial calculator, make sure to convert quarterly compounding to the equivalent annual rate.

4. **Calculation:**

After inputting these values into the TVM Solver and solving for I/Y, the resulting annual interest rate is approximately 4.52%.

Therefore, the correct annual interest rate is **4.52 percent**.

If you need a detailed explanation or have any questions, feel free to ask!

### Additional Questions:
1. How does the compounding frequency affect the total interest paid over the life of a loan?
2. What would the monthly payment be if the interest rate were 6.91% instead?
3. How can you calculate the total interest paid over the 20-year period for this loan?
4. What is the effect of making extra payments on the total interest paid?
5. How does the length of the loan term affect the monthly payment and total interest paid?

### Tip:
When comparing loans, always consider both the interest rate and the compounding frequency, as these can significantly impact the total cost of the loan.

What is the annual interest rate on a twenty-year $52300 car loan that is compounded quarterly and has monthly payments of $283.61?

Determine the annual interest rate for a twenty-year car loan of $52,300, with monthly payments of $283.61, compounded quarterly. Learn how to use the Time Value of Money (TVM) formula and calculate the interest rate, suitable for high school or college students.

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