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 (also known as the internal rate of return, IRR) on a lease, we need to solve for the rate that equates the present value of the lease payments to the value of the truck plus the $1 buyout at the end. Here's how we approach it:

### Key Information:
- **Truck cost (present value of the lease):** $170,000
- **Down payment:** $0
- **Monthly payment:** $4,000
- **Lease term:** 5 years (or 60 months)
- **Buyout option:** $1 at the end of the lease
- **Effective interest rate (r):** The unknown variable we need to solve for.

### Formula:
The formula for the present value of an annuity with additional final payment is:

\[
\text{Present Value} = \sum \left( \frac{\text{Monthly Payment}}{(1 + r)^{t}} \right) + \frac{\text{Buyout}}{(1 + r)^{n}}
\]

Where:
- $r$ is the monthly interest rate
- $t$ is the month number (1, 2, ..., 60)
- $n$ is the total number of months (60)
- The present value is $170,000
- The buyout is $1

Let's solve for the effective interest rate using this equation by trial and error or through a numerical solver.

I'll calculate it for you.The effective annual interest rate on the lease is approximately **15.51%**.

Would you like more details on the calculation or any clarifications?

Here are five related questions to expand your understanding:
1. How does the monthly interest rate compare to the annual interest rate?
2. What are the advantages of calculating the internal rate of return (IRR) on leases?
3. How does the buyout option affect the overall cost of leasing?
4. What impact does the lease term have on the effective interest rate?
5. How would a down payment influence the interest rate?

**Tip:** Always compare the effective interest rate with other financing options (e.g., loans) to ensure you're getting the best deal.

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?

Find the effective interest rate for leasing a $170,000 truck with no down payment, $4,000 monthly payments for 5 years, and a $1 buyout option. This solution uses the annuity formula and internal rate of return (IRR) concepts, ideal for students in financial mathematics or business calculus.

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