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 a lease, we need to first understand the financial structure of the lease. Here's the breakdown:

- **Truck cost**: $170,000
- **Monthly payment**: $4,000
- **Lease term**: 5 years (or 60 months)
- **Buyout option at the end**: $20,000

We'll approach this in several steps:
1. **Find the total payments**.
2. **Estimate the interest rate** by treating this problem as a present value (PV) of annuities plus the final balloon payment (buyout).

### 1. Total Payments:
Over the 5-year period, the total payment is calculated as:
\[
\text{Total payments} = 60 \times 4,000 = 240,000
\]
Adding the buyout amount:
\[
\text{Total outlay} = 240,000 + 20,000 = 260,000
\]

### 2. Interest Rate Calculation:
The lease can be viewed as a loan where:
- Principal (Present Value, PV) = $170,000
- Monthly payments = $4,000
- Number of periods (n) = 60
- Final payment (Buyout) = $20,000

Using the **present value of annuities** formula, combined with a final payment (balloon):
\[
PV = P \times \left(1 - (1 + r)^{-n}\right) / r + F \times (1 + r)^{-n}
\]
Where:
- $ P $ is the monthly payment
- $ r $ is the monthly interest rate
- $ n $ is the number of payments
- $ F $ is the final payment

Now let's calculate the effective interest rate by solving this equation.The effective annual interest rate on the lease is approximately **18.25%**.

Would you like further details or explanations on this? Here are 5 related questions to expand on the topic:

1. How is the present value of annuities used in finance?
2. What are the differences between nominal and effective interest rates?
3. How can the effective interest rate impact total payments on a loan or lease?
4. Can you break down how the monthly interest rate was derived from this calculation?
5. What are alternative methods to finance a vehicle and their cost implications?

**Tip**: When comparing loan or lease offers, always check the effective interest rate, as it reflects the true cost of borrowing after compounding!

Learn how to calculate the effective interest rate on a lease for a $170,000 truck with a $4,000 monthly payment over 5 years and a $20,000 buyout option at the end. This solution covers key financial concepts such as the present value of annuities and the effective interest rate. The final interest rate is approximately 18.25%.

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