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 calculate the **effective interest rate** (also known as the **internal rate of return (IRR)**) for the lease, we need to solve for the rate $ r $ that makes the net present value (NPV) of the lease cash flows equal to zero.

Here are the details we have:

- **Truck price (initial value)** = $170,000
- **Monthly payment** = $4,000
- **Term** = 5 years = 60 months
- **End-of-lease Fair Market Value (FMV)** = $40,000
- **Down payment** = $0

We assume the payments are made at the end of each month. To calculate the effective interest rate, we treat this as a type of **amortized loan** where:

- You are making regular monthly payments of $4,000.
- At the end of the lease, the truck has a balloon payment (FMV) of $40,000.
  
The equation for calculating the interest rate for such a lease is based on the formula for the present value of an annuity plus the discounted value of the balloon payment.

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Here are five questions to expand on this topic:
1. What is the difference between nominal and effective interest rates?
2. How does the internal rate of return (IRR) differ from the interest rate?
3. How can a balloon payment affect the total cost of leasing or financing a vehicle?
4. What other methods can be used to calculate lease interest rates?
5. How does a down payment influence the interest calculation in a lease?

Tip: Always compare the effective interest rate with the nominal rate when evaluating lease offers!

Learn how to calculate the effective interest rate (IRR) for a truck lease priced at $170,000 with $4,000 monthly payments over 5 years and a $40,000 Fair Market Value (FMV) at the end. Understand key financial concepts such as present value, annuities, and the internal rate of return (IRR). Suitable for students and professionals in financial mathematics.

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