What is the effective interest rate on a lease for a $170,000 truck with $0 down, $4,000 monthly payment over 5 years, no buy-out option, and $40,000 truck FMV after 5 years?

To find the **effective interest rate** (also known as the implicit interest rate) on the lease, we need to approach this as a **time value of money** problem. The payments made over the life of the lease, and the value of the truck at the end of the lease (which is the **residual value**), need to be balanced to figure out the interest rate embedded in the payments.

The **given details**:
- **Truck price (Present Value)**: $170,000
- **Monthly payment**: $4,000
- **Lease term**: 5 years (60 months)
- **Residual value (Future Value)**: $40,000
- **Down payment**: $0
- **No buy-out option**

We will use the following formula to calculate the interest rate:

\[
PV = \frac{PMT \times (1 - (1 + r)^{-n})}{r} + \frac{FV}{(1 + r)^n}
\]

Where:
- $PV$ is the present value (the truck price, $170,000),
- $PMT$ is the monthly payment ($4,000),
- $r$ is the monthly interest rate (which we need to find),
- $n$ is the number of payments (60 months),
- $FV$ is the future value or residual value ($40,000).

I'll now calculate the effective interest rate.The **effective annual interest rate** on the lease is approximately **20.68%**.

Would you like further details or clarifications on this? Here are some related questions you might find useful:

1. How is the monthly interest rate related to the annual effective interest rate?
2. What is the difference between nominal and effective interest rates?
3. How does the residual value affect the lease interest rate?
4. How can I calculate the lease interest rate if there is a down payment?
5. What is the impact of varying the lease term on the interest rate?

**Tip:** The higher the residual value (future value of the asset), the lower your monthly payment typically is, assuming all other factors remain constant.

Learn how to calculate the effective interest rate for a truck lease with a $170,000 value, $4,000 monthly payments over 5 years, and a $40,000 residual value. This detailed guide covers key time value of money concepts and interest rate formulas. Ideal for college-level finance students or advanced high school learners.

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