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 calculate the **effective interest rate (EIR)** on a lease, we can treat the lease as a type of loan and solve for the interest rate that makes the present value of the payments equal to the cost of the truck.

Here’s how we can break down the problem:

1. **Truck price**: $170,000 (Present Value)
2. **Monthly payment**: $4,000
3. **Lease term**: 5 years = 60 months
4. **Buy-out option**: $1 at the end
5. **Down payment**: $0

We are solving for the interest rate (usually denoted as "r") that makes the present value of the lease payments and the buy-out option equal to the truck's cost.

This can be written as a **Present Value of an Annuity formula**:

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

Where:
- $ PV $ is the truck price ($170,000),
- $ P $ is the monthly payment ($4,000),
- $ r $ is the monthly interest rate (which we’ll solve for),
- $ n $ is the total number of payments (60 months),
- $ F $ is the future buy-out value ($1).

Let me calculate the interest rate using this formula.The effective annual interest rate (EIR) on the lease for the truck is approximately **15.51%**.

Would you like more details or have any questions?

Here are 5 related questions:
1. How would increasing the monthly payment affect the interest rate?
2. What happens to the effective interest rate if the lease term changes to 4 years?
3. Can the same formula be used for a loan with an upfront down payment?
4. What is the difference between nominal interest rate and effective interest rate?
5. How does leasing compare to financing in terms of total cost?

**Tip**: When comparing loan or lease options, always check the effective interest rate, as it considers the compounding effect, giving you a clearer view of the true cost.

Learn how to calculate the effective interest rate for a lease on a $170,000 truck with $0 down, $4,000 monthly payment over 5 years, and a $1 buy-out option. This solution breaks down the present value of annuity formula and the key steps involved, suitable for finance students.

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