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** on a lease, we can treat it similarly to a loan. Since the lease has a fixed monthly payment of $4,000 for 5 years (60 months) with a $1 buy-out option at the end, we can apply the following approach:

### Steps to calculate the effective interest rate:
1. **Present Value (PV):** The value of the truck is $170,000, which is essentially the loan principal.
2. **Payment (PMT):** The monthly payment is $4,000.
3. **Number of Periods (N):** The duration of the lease is 5 years, so there are 60 months (5 × 12).
4. **Future Value (FV):** At the end of the lease, you have a $1 buy-out option, which means the future value is $1.

We can use the following formula for the **interest rate per period** in a loan amortization:

\[
PV = PMT \times \left( 1 - (1 + r)^{-N} \right) / r + FV / (1 + r)^N
\]

Where:
- $ PV $ = Present value of the loan (or lease)
- $ PMT $ = Monthly payment
- $ N $ = Number of monthly payments (periods)
- $ r $ = Monthly interest rate (what we are solving for)
- $ FV $ = Future value of the loan

We can solve for $ r $ (the monthly interest rate), then multiply by 12 to get the annual **effective interest rate**.

Let me calculate the value for you.The effective annual interest rate on the lease is approximately **14.50%**.

Would you like more details or have any further questions?

Here are 5 related questions that expand on this concept:
1. How does the buy-out option affect the overall cost of the lease?
2. What is the difference between nominal and effective interest rates?
3. How would a down payment change the calculation of the effective interest rate?
4. What factors influence whether leasing or buying is more financially favorable?
5. Can the effective interest rate be negative in some financial agreements?

**Tip:** When comparing financing options, always calculate the effective interest rate to understand the true cost of borrowing.

Calculate the effective interest rate for a $170,000 truck lease with $0 down, $4,000 monthly payment for 5 years, and a $1 buy-out option. Learn key concepts in financial mathematics including loan amortization and interest rate calculations. Suitable for advanced high school or college-level students.

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