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 (often referred to as the internal rate of return, or IRR) on a lease, we treat the series of lease payments as a loan with the truck's value as the principal. The lease payments act like loan payments, and the final $1 buy-out is similar to a balloon payment.

Here's how we approach this:

### Data:
- **Truck Price (Principal)**: \$170,000
- **Monthly Payment**: \$4,000
- **Term**: 5 years (60 months)
- **Buy-out Option**: \$1 at the end

### Calculation:

The interest rate $ r $ (monthly effective rate) must satisfy the following equation:

\[
170,000 = \sum_{i=1}^{60} \frac{4000}{(1 + r)^i} + \frac{1}{(1 + r)^{60}}
\]

This equation sums up the present values of each monthly payment and the final buy-out, which should equal the principal of \$170,000.

Now let's calculate the monthly effective interest rate and then annualize it to find the effective annual interest rate.

I'll proceed with the computation.The effective annual interest rate on the lease is approximately **15.51%**.

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

Here are 5 related questions for further exploration:
1. How does the effective interest rate compare to a nominal interest rate in leases?
2. What factors can influence the effective interest rate in lease agreements?
3. How does a larger or smaller monthly payment affect the interest rate calculation?
4. What is the difference between leasing and financing in terms of overall cost?
5. How does a buy-out option at the end of a lease impact the total cost?

**Tip:** Always compare the effective interest rate when considering different lease options to understand the true cost of financing.

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?

Discover how to calculate the effective interest rate on a lease for a $170,000 truck with $0 down, $4,000 monthly payments over 5 years, and a $1 buy-out option. Understand key financial concepts such as Internal Rate of Return (IRR) and present value calculations.

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