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 $20,000 buy-out option at the end?

To find the effective interest rate (or implied interest rate) on the lease, we can use the following information:

- **Truck price (Present Value, PV):** $170,000
- **Monthly payment (PMT):** $4,000
- **Number of payments (n):** 60 months (5 years)
- **Buy-out option (Future Value, FV):** $20,000
- **Down payment:** $0

We need to calculate the interest rate that would result in these monthly payments using the formula for a lease or loan:

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

Where:
- $ r $ is the monthly interest rate (which we can later convert to an annual rate).
- $ PV $ is the present value (truck cost, $170,000).
- $ PMT $ is the monthly payment ($4,000).
- $ FV $ is the future value (buy-out option, $20,000).
- $ n $ is the number of payments (60).

We will solve for $ r $ iteratively or using numerical methods. Let me calculate that.The effective annual interest rate on the lease is approximately **18.25%**.

Would you like more details or have any questions about the process?

Here are 5 related questions to expand on this topic:
1. How does the buy-out option affect the overall cost of a lease?
2. What are the advantages of leasing a truck compared to purchasing it with a loan?
3. How does the effective interest rate change with a down payment?
4. Can the interest rate differ between different types of leases (closed-end vs. open-end)?
5. How do monthly payments change if the lease term is shorter or longer?

**Tip:** Always compare the effective interest rate of a lease to other financing options to evaluate its cost-efficiency.

Discover how to calculate the effective interest rate for a lease involving a $170,000 truck with $0 down, $4,000 monthly payments over 5 years, and a $20,000 buy-out option at the end. This step-by-step solution covers key financial concepts, including lease payment formulas and interest rate calculations. Suitable for Grades 11-12 or college-level students.

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