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 $40,000 buy-out option at the end?

To determine the effective interest rate on the lease, we need to think of this problem as a time value of money calculation. The key elements here are:

- **Truck price (PV)**: $170,000 (present value of the truck)
- **Monthly payment (PMT)**: $4,000
- **Lease term**: 5 years (60 months)
- **Buy-out option (FV)**: $40,000 (future value, i.e., the price you pay to purchase the truck at the end of the lease)

We will calculate the **effective interest rate** by finding the internal rate of return (IRR) for these cash flows.

The formula for the lease can be represented as:

\[
PV = \sum_{t=1}^{60} \frac{PMT}{(1+r)^t} + \frac{FV}{(1+r)^{60}}
\]

Where:
- $ PV $ is the present value of the truck ($170,000)
- $ PMT $ is the monthly payment ($4,000)
- $ r $ is the monthly interest rate
- $ FV $ is the buy-out option ($40,000)

Let me calculate the effective interest rate using these inputs.The effective annual interest rate on the lease is approximately **20.68%**.

Would you like to dive deeper into any part of this calculation, or do you have further questions? Here are five related questions that might interest you:

1. How does the interest rate change if the monthly payment is altered?
2. What is the difference between nominal and effective interest rates?
3. How would the effective interest rate change if a down payment is included?
4. Can we calculate the total cost of leasing this truck?
5. How is the interest rate affected by the buy-out option value?

**Tip:** When leasing, always consider the buy-out option, as it significantly impacts the overall cost and the effective interest rate.

Find the effective interest rate for leasing a $170,000 truck with a $4,000 monthly payment over 5 years and a $40,000 buy-out option at the end. Learn how time value of money and the internal rate of return (IRR) concept apply to this calculation.

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