What is the effective interest rate on the truck costing $170000 with $4000 montly payment for 5 years and $20,000 buy-out option at the end?*

To calculate the **effective interest rate** for a loan with monthly payments and a final buy-out option, we must treat this as a **loan with fixed monthly payments and a balloon payment** at the end.

### Given Information:
- **Cost of truck (Principal)**: \$170,000
- **Monthly Payment**: \$4,000
- **Loan Term**: 5 years (or 60 months)
- **Balloon Payment (Buy-out option)**: \$20,000
- **Number of payments**: 60 months

### Steps to Calculate Effective Interest Rate:
1. **Determine the loan amount to be financed**: The total cost of the truck is \$170,000, but we are assuming the balloon payment of \$20,000 will be paid at the end, so the financed amount is the difference between the two:
   \[
   \text{Financed Amount} = 170,000 - 20,000 = 150,000
   \]

2. **Using the annuity formula** for monthly payments:
   The formula to calculate the monthly payment for a loan is:
   \[
   P = \frac{r \times PV}{1 - (1 + r)^{-n}}
   \]
   Where:
   - $P$ = monthly payment = \$4,000
   - $r$ = monthly interest rate (which we need to find)
   - $PV$ = present value (financed amount) = \$150,000
   - $n$ = total number of payments = 60 months

3. **Adjust for the balloon payment**: We need to include the fact that there's a balloon payment of \$20,000 at the end of the 60th month.

### Solving for $r$:
We need to solve for $r$, which involves either using a **financial calculator** or an **iterative process** to determine the effective monthly interest rate that satisfies this equation.

Let me compute this for you.The **effective annual interest rate** for the truck loan is approximately **24.94%**.

This rate takes into account the monthly payments of \$4,000 over 5 years and the final buy-out (balloon payment) of \$20,000 at the end of the term.

Would you like more details, or do you have any questions about this calculation?

Here are 5 related questions to expand on this:
1. How would the interest rate change with a larger down payment?
2. What is the total interest paid over the life of this loan?
3. How does the balloon payment affect the total cost of the loan?
4. What is the difference between nominal and effective interest rates?
5. How can prepaying part of the loan affect the total interest paid?

**Tip:** Effective interest rates consider compounding, which often results in a higher rate compared to the nominal rate.

What is the effective interest rate on the truck costing $170,000 with $4,000 monthly payment for 5 years and $20,000 buy-out option at the end?

Learn how to calculate the effective interest rate for a $170,000 truck loan with $4,000 monthly payments over 5 years and a $20,000 buy-out option. This problem explores loan amortization, balloon payments, and effective interest rates using the annuity formula. Suitable for college-level finance or math students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation