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 $20000 buy-out option at the end?

To calculate the effective interest rate (EIR) on a lease, we can treat it similarly to a loan problem and use an approach based on the **Internal Rate of Return (IRR)**. Here, we'll break the problem into components:

### Lease Details:
- **Truck price (principal):** \$170,000
- **Monthly payment:** \$4,000
- **Lease duration:** 5 years (60 months)
- **Buy-out option at the end:** \$20,000
- **Down payment:** \$0

The effective interest rate is found by calculating the rate $ r $ that equates the present value of all the payments (monthly payments + buyout option) to the price of the truck.

Mathematically, this can be represented as:

\[
P = \sum_{t=1}^{60} \frac{4000}{(1+r)^t} + \frac{20000}{(1+r)^{60}}
\]

Where:
- $ P = 170,000 $ (initial value of the truck)
- $ r $ is the monthly interest rate, and we convert it to an annual rate at the end.

I will now calculate this using a numerical approach to solve for $ r $.The effective annual interest rate on the lease is approximately **18.25%**.

Would you like further clarification or more details about this calculation?

Here are 5 related questions for further exploration:
1. How does the effective interest rate change if there is a down payment?
2. What is the difference between nominal and effective interest rates?
3. How would the lease terms change if the buyout option were reduced?
4. How does changing the lease duration affect the effective interest rate?
5. How does leasing compare to financing a vehicle purchase?

**Tip:** Always consider the total cost of a lease, including monthly payments, interest, and the buyout option, when comparing it to other financing options.

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?

Find out how to calculate the effective interest rate on a truck lease with $170,000 principal, $4,000 monthly payments over 5 years, and a $20,000 buyout option at the end. This problem uses interest rate calculations and the internal rate of return (IRR) method.

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