What is the effective interest rate on a lease for a $170,000 truck with $0 down, $4,000 monthly payment over 5 years, and $1 buy-out option at the end?

To find the effective interest rate on a lease, we can treat this as a type of loan amortization problem, where the lease payments (monthly payments) are treated as installments on a loan. The key components are:

- Truck price (principal): $170,000
- Monthly payment: $4,000
- Lease term: 5 years = 60 months
- Buy-out option at the end: $1 (essentially treated as a negligible cost)

We can solve for the effective interest rate using the following formula for the monthly payment on an amortizing loan:

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

Where:
- $P$ is the monthly payment ($4,000)
- $r$ is the monthly interest rate (what we are solving for)
- $PV$ is the present value or principal ($170,000)
- $n$ is the total number of payments (60 months)

Now, let's solve for the effective interest rate using this equation. I'll calculate it for you.The effective annual interest rate on the lease is approximately **15.51%**.

Would you like further clarification on how this was calculated or any other details?

Here are five related questions you might find interesting:
1. How does the lease term affect the effective interest rate?
2. What is the difference between nominal and effective interest rates?
3. How would a down payment influence the effective interest rate?
4. What happens to the interest rate if the monthly payment is adjusted?
5. How can you compare different lease offers using the effective interest rate?

**Tip:** When evaluating lease or loan options, always compare the effective interest rate rather than the nominal rate to understand the true cost.

Calculate the effective interest rate on a $170,000 truck lease with $0 down, $4,000 monthly payments over 5 years, and a $1 buy-out. This problem involves amortization and the loan payment formula, helping users understand how interest rates are determined in lease agreements.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation