calculate the effective interest rate on a lease for a $170000 truck with 0 down for $4000, monthly payment over 5 years, and $20000 buyout option at the end

To calculate the **effective interest rate** on a lease, we can follow these steps:

1. **Identify key variables**:
   - **Vehicle price (Principal)**: $170,000
   - **Monthly payment**: $4,000
   - **Lease term**: 5 years = 60 months
   - **Residual value (buyout option)**: $20,000 at the end of the lease
   - **Down payment**: $0 (no initial down payment)

2. **Interpret the problem**: 
   - We are essentially calculating the interest rate on a loan where the truck costs $170,000, with monthly payments of $4,000, and a $20,000 lump-sum payment at the end.
   - The key here is to treat this as a loan where the payments are structured as specified.

3. **Formulation**: 
   - We need to calculate the **internal rate of return (IRR)** that equates the present value of all lease payments, including the buyout option at the end, to the vehicle’s price.
   
   The equation will be in the form:

   \[
   170,000 = \sum_{t=1}^{60} \frac{4000}{(1+r)^t} + \frac{20,000}{(1+r)^{60}}
   \]
   where $ r $ is the effective monthly interest rate, and then we will convert it into the **annual interest rate**.

Let me compute that for you.

Calculate the effective interest rate on a lease for a $170,000 truck with 0 down for $4,000, monthly payment over 5 years, and $20,000 buyout option at the end.

Learn how to calculate the effective interest rate on a lease for a $170,000 truck with $4,000 monthly payments over 5 years, and a $20,000 buyout option at the end. This solution involves key concepts such as IRR (Internal Rate of Return) and Present Value calculations. Suitable for college-level students.

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