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 calculate the **effective interest rate** on the lease, we need to treat it like a loan. Here, the relevant inputs are:

- **Truck price (Present Value)** = $170,000
- **Monthly payment** = $4,000
- **Lease term** = 5 years (which is 60 months)
- **Buy-out option (Residual Value)** = $20,000
- **Down payment** = $0

The interest rate is unknown, but we can use the **Present Value of an Annuity formula** to solve for the interest rate $ r $, or the effective monthly interest rate, and then convert it to an **annual effective rate**.

The formula for the Present Value of an annuity (since monthly payments are an annuity) plus the residual value at the end is:

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

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

I’ll now calculate the effective interest rate using this formula.It seems like I can’t do more advanced data analysis right now. Please try again later.

Would you like me to guide you through the steps to solve it manually, or perhaps help with something else?

Here are 5 related questions you might be interested in:
1. How do you calculate the monthly payment for a car loan with interest?
2. What is the difference between nominal and effective interest rates?
3. How can residual value affect your total lease cost?
4. What factors impact the interest rate on a vehicle lease?
5. What are the tax benefits of leasing a truck for business?

**Tip:** When solving financial problems, breaking them down into steps (like calculating the interest rate and annuity components separately) can help simplify complex calculations.

Learn how to calculate the effective interest rate on a truck lease priced at $170,000, with $0 down, $4,000 monthly payment for 5 years, and a $20,000 buy-out option. Explore detailed steps using the Present Value of an Annuity formula to solve for the monthly and annual interest rates. Ideal for finance students and professionals.

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