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 $1 buy-out option at the end?

To calculate the **effective interest rate** on a lease, we treat this like a loan amortization problem where the lease payments cover the cost of the truck with interest over the term, and there is a nominal $1 buy-out at the end.

### Given information:
- **Truck price (Principal)** = $170,000
- **Monthly payment** = $4,000
- **Lease term** = 5 years (or 60 months)
- **Buy-out option** = $1 at the end

We need to calculate the effective interest rate (annual percentage rate, or APR) for these terms. Here's the approach:

1. The **monthly lease payment** ($4,000) includes both the principal and interest payments.
2. The **principal** of $170,000 is paid over **60 months**, with $1 as the residual value.
3. The effective interest rate is the rate that equates the present value of the monthly payments to the value of the truck.

We can use the formula for the present value of an annuity to calculate this. The equation is:

\[
P = \frac{R \times (1 - (1 + i)^{-n})}{i} + \frac{F}{(1 + i)^n}
\]

Where:
- $P$ = Present value (truck price, $170,000)
- $R$ = Monthly payment ($4,000)
- $i$ = Monthly interest rate (we will solve for this)
- $n$ = Number of months (60)
- $F$ = Future value (residual buyout, $1)

Let me solve for the interest rate $i$.The effective annual interest rate (APR) on the lease is approximately **14.50%**.

Would you like further details on the calculation, or do you have any questions?

Here are 5 related questions that can extend your understanding:
1. How does changing the lease term affect the interest rate?
2. What happens if there is a down payment on the lease?
3. How is the effective interest rate different from the nominal rate?
4. How would this calculation change for different monthly payments?
5. What would the effective interest rate be with a higher buy-out price?

**Tip:** When comparing lease offers, always consider the effective interest rate (APR), as it reflects the true cost of financing.

Calculate the effective interest rate (APR) for a $170,000 truck lease with a $4,000 monthly payment over 5 years and a $1 buy-out option at the end. This detailed solution uses loan amortization and the present value of annuity formula to find the effective rate of 14.50%.

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