Calculate what is the effective interest rate on a lease for a $170000 truck with 0 down for $4000, monthly payment over 5 years, and $1 buyout option at the end

To calculate the effective interest rate (also known as the internal rate of return, or IRR) for this truck lease, we follow these steps:

### Given Data:
- Truck cost (Principal): $170,000
- Down payment: $0
- Monthly payment: $4,000
- Lease term: 5 years = 60 months
- Residual (buyout) amount at the end of lease: $1
- We want to calculate the effective interest rate on this lease.

The payments structure essentially represents an amortizing loan, where you're making equal payments every month and paying a nominal amount ($1) at the end to take ownership.

### Step-by-Step Calculation:
The formula to calculate the effective interest rate involves solving for the rate $ r $ that satisfies the following equation:

\[
PV = \sum_{i=1}^{60} \frac{PMT}{(1 + r)^i} + \frac{FV}{(1 + r)^{60}}
\]

Where:
- $ PV $ is the present value or the cost of the truck ($170,000)
- $ PMT $ is the monthly payment ($4,000)
- $ r $ is the monthly interest rate (which we'll solve for)
- $ FV $ is the future value or residual amount at the end ($1)
- $ i $ is the month number

The effective annual interest rate can be derived once we find $ r $.

Let me now compute the effective monthly and annual interest rate by solving this equation.The effective interest rates for the lease are:

- **Monthly interest rate**: 1.21%
- **Annual effective interest rate**: 15.51%

This is the rate of return the lender earns on this lease given the payment terms.

Would you like more details on any specific part of the calculation? Here are some related questions you might consider:

1. How is the monthly interest rate different from the annual rate?
2. What does the internal rate of return (IRR) signify in lease agreements?
3. How does the residual buyout option affect the total cost of the lease?
4. Can the interest rate be calculated differently for a loan vs. a lease?
5. What happens if there's a down payment—how does it affect the rate?

**Tip**: For more accurate financial planning, always compare the effective annual interest rate, not just the nominal rates, when evaluating lease or loan offers.

Learn how to calculate the effective interest rate on a lease for a $170,000 truck with 0 down, $4000 monthly payments for 5 years, and a $1 buyout option. This step-by-step solution involves key finance concepts like amortization and internal rate of return (IRR).

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