What is the effective interest rate on a lease for a $170,000 truck with $0 down, $4,000 monthly payment over 5 years,  except no buy-out option at the end of the lease and $40,000 truck FMV after 5 years?

To calculate the **effective interest rate** on the lease, we will treat the lease as a type of loan and solve for the implicit interest rate using a financial formula. The given lease is structured with no down payment, monthly payments, and a residual value (FMV) at the end, which makes it similar to a type of amortization loan with a balloon payment at the end.

### Key information:
- Truck cost (present value, $PV$): $170,000
- Monthly lease payment: $4,000
- Lease term: 5 years (60 months)
- Residual value (future value, $FV$): $40,000
- No buy-out option at the end of the lease
- Effective interest rate: to be determined

We will use the formula for the present value of an amortizing loan:

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

Where:
- $PV$ is the present value of the truck ($170,000),
- $PMT$ is the monthly payment ($4,000),
- $r$ is the monthly interest rate (what we need to find),
- $n$ is the number of periods (60 months),
- $FV$ is the residual value ($40,000).

We can rearrange this formula to solve for $r$, but because it's non-linear, we'll need to use numerical methods or iterative approaches to find the exact interest rate.

Let me compute the effective interest rate for you.The effective annual interest rate on the lease is approximately **20.68%**.

Would you like any additional details on how this was calculated or a deeper breakdown of the process?

Here are 5 questions to extend this topic:
1. How does the residual value (FMV) affect the interest rate calculation?
2. What are the differences between nominal and effective interest rates?
3. How would adding a down payment change the effective interest rate?
4. Can a lease with no buy-out option still be advantageous over buying outright?
5. How does the term length (in months or years) affect the interest rate?

**Tip:** When comparing leases to loans, always consider the residual value and interest rate to determine the most cost-effective option.

What is the effective interest rate on a lease for a $170,000 truck with $0 down, $4,000 monthly payment over 5 years, except no buy-out option at the end of the lease and $40,000 truck FMV after 5 years?

Calculate the effective interest rate on a $170,000 truck lease with no down payment, $4,000 monthly payments over 5 years, and a $40,000 residual value. This problem involves financial mathematics, amortization, and interest rate calculations suitable for finance students.

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