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 for a truck, we'll treat the lease as a financing problem and calculate the implicit interest rate (also known as the internal rate of return, or IRR) on the loan. Here are the key points for the problem:

- **Lease amount (Principal):** $170,000
- **Monthly payment:** $4,000
- **Lease term:** 5 years (60 months)
- **Residual value (buy-out option):** $1

We can think of the lease as a loan where the truck's value is being repaid in monthly installments, with a final payment of $1 at the end. To find the effective interest rate, we need to find the interest rate that equates the present value of the payments with the value of the truck.

### Formula for the Present Value of an Annuity:

We can express the total lease amount as the present value of the monthly payments. The present value (PV) of the monthly lease payments is calculated using the following formula:

\[
PV = PMT \times \left( 1 - \frac{1}{(1 + r)^n} \right) \div r
\]

Where:
- $PMT$ is the monthly payment ($4,000),
- $r$ is the monthly interest rate (annual interest rate divided by 12),
- $n$ is the total number of months (60 months for a 5-year term).

The sum of the present value of the payments should equal the initial loan amount, $170,000.

I’ll calculate the implicit interest rate for this lease.The effective annual interest rate (or implicit interest rate) on the lease is approximately **15.51%**.

This rate reflects the cost of financing the truck through the lease payments, considering the $4,000 monthly payments over 5 years and the $1 buy-out option at the end.

Would you like more details, or do you have any other questions?

Here are some related questions:
1. How does the interest rate affect the overall cost of the lease?
2. What is the total amount paid over the 5-year lease term?
3. How would a down payment affect the effective interest rate?
4. How would a higher or lower residual value change the interest rate calculation?
5. How can you compare this lease's interest rate with financing options?

**Tip:** When leasing a vehicle, understanding the effective interest rate helps you compare the cost of leasing versus buying directly or financing through a loan.

Find out how to calculate the effective interest rate (IRR) on a $170,000 truck lease with $4,000 monthly payments over 5 years, including a $1 buy-out option. Learn the key formulas and steps involved in determining the implicit interest rate.

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