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 determine the effective interest rate (or the implied rate of interest) on this lease, we need to consider the lease payments, the buyout option, and the structure of the cash flows over time.

### Given:
- **Truck Price (Present Value, PV):** $170,000
- **Monthly Payment (PMT):** $4,000
- **Lease Term:** 5 years (60 months)
- **Buyout Option (Future Value, FV):** $20,000
- **Down Payment:** $0

### Objective:
We aim to find the effective interest rate, $ r $, which satisfies the present value of all payments (including the buyout) equal to the truck price.

We can model this lease as a loan with monthly payments and a lump sum payment (the buyout option) at the end. The formula for the present value of an annuity (the lease payments) plus the present value of the future value (the buyout option) is:

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

Where:
- $ PV $ is the present value ($170,000),
- $ PMT $ is the monthly payment ($4,000),
- $ FV $ is the future value (buyout option of $20,000),
- $ r $ is the monthly interest rate,
- $ n $ is the number of periods (60 months).

The solution involves solving this equation for $ r $, which can be done iteratively or using a financial calculator. I'll compute the interest rate for you.The effective annual interest rate on the lease is approximately **18.25%**.

Would you like further details or clarifications?

Here are 5 related questions:
1. How does the effective interest rate compare to the nominal interest rate?
2. What would happen to the interest rate if the buyout option changed?
3. How can we calculate the total cost of the lease over 5 years?
4. What impact would a down payment have on the effective interest rate?
5. How is the present value formula applied in other financial contexts?

**Tip:** Understanding how to compute interest rates on leases can help you compare financing options effectively.

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?

Calculate the effective interest rate on a $170,000 truck lease with $4,000 monthly payments over 5 years and a $20,000 buyout option at the end. This problem covers key financial concepts such as present value, annuities, and effective interest rates, suitable for finance and economics students.

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