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 (often referred to as the implicit interest rate) on a lease, we need to model the lease payments as a loan with regular monthly payments and a residual value at the end (in this case, the $20,000 buy-out option).

Here’s how to approach it:

### Variables:
- **Principal (P)**: $170,000 (cost of the truck)
- **Monthly Payment (PMT)**: $4,000
- **Number of Payments (n)**: 5 years × 12 months = 60 payments
- **Residual Value (RV)**: $20,000
- **Down Payment**: $0

We need to find the **interest rate (r)** that satisfies this lease setup.

The lease can be modeled using the **Present Value of an Annuity** formula with a residual value at the end:

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

This equation is hard to solve algebraically, so it usually requires numerical methods to find $ r $.

I'll calculate the interest rate numerically.The effective annual interest rate for the lease is approximately **18.25%**.

Would you like more details on how this was calculated or have any further questions?

Here are 5 related questions to deepen your understanding:
1. How is the effective interest rate different from the nominal interest rate?
2. What factors affect the total cost of leasing vs. buying a vehicle?
3. How does a residual value impact monthly payments in a lease?
4. What is the formula for calculating the present value of an annuity?
5. How do interest rates influence leasing terms?

**Tip:** In leasing, a higher residual value typically results in lower monthly payments but may lead to higher costs if you decide to buy the asset at the end.

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 for a $170,000 truck lease with $4,000 monthly payments over 5 years and a $20,000 buy-out option. This example uses the present value of annuity formula and explains how to determine the interest rate using numerical methods. Suitable for finance and business math students.

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