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 $40,000 FMV at the end?

To find the effective interest rate on the lease, we can use the concept of the **Internal Rate of Return (IRR)** or **Effective Interest Rate** (EIR), which equates the present value of the lease payments to the truck's cost. Here's how we'll approach this:

### Given Data:
- **Truck Cost** (Present Value, PV): $170,000
- **Monthly Payment**: $4,000
- **Lease Term**: 5 years (which is 60 months)
- **Fair Market Value (FMV) at the End of Lease**: $40,000
- **Down Payment**: $0

The formula to solve for the effective interest rate ($r$) involves finding the rate at which the present value of the lease payments and the balloon payment (FMV) equals the truck's cost.

### Lease Payment Structure:
1. Monthly payments of $4,000 over 60 months.
2. Balloon payment (FMV) of $40,000 at the end of the lease.

The present value of these cash flows should equal $170,000. We need to solve the following equation to find the interest rate $r$:

\[
170,000 = \sum_{i=1}^{60} \frac{4,000}{(1+r)^i} + \frac{40,000}{(1+r)^{60}}
\]

This is a complex equation that can be solved using numerical methods (such as Newton's method or trial and error). I will calculate it for you.

Let me compute the effective interest rate.The effective interest rate on the lease is approximately **18.95%**.

This rate reflects the cost of the lease considering the monthly payments of $4,000 and the $40,000 balloon payment at the end of the 5-year term.

Would you like more details on this calculation or have any further questions?

Here are five related questions:
1. How does the effective interest rate differ from the nominal interest rate?
2. What happens to the interest rate if you make a down payment?
3. How would increasing the residual value affect the effective interest rate?
4. Can you compare leasing vs. buying the truck based on this interest rate?
5. How can you calculate the total cost of leasing, including the interest?

**Tip:** The effective interest rate includes the impact of compounding, making it a better reflection of actual borrowing costs compared to the nominal rate.

Learn how to calculate the effective interest rate for a $170,000 truck lease with $0 down, $4,000 monthly payments over 5 years, and a $40,000 fair market value (FMV) at the end. This solution uses financial mathematics, including IRR and present value concepts, and is suitable for college-level or advanced high school students.

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