Jennifer is leasing a car from a local auto retailer. The terms of the lease include a 9% interest rate for 36 months with a residual value of 57%. The MSRP for the car Jennifer is leasing is $17,500. What will Jennifer’s monthly lease payment be?
The Correct Answer and Explanation is
To calculate Jennifer’s monthly lease payment, we need to use the standard lease payment formula which includes:
- Depreciation Fee
- Finance Fee
- Total Monthly Lease Payment
Given:
- MSRP (Capitalized Cost) = $17,500
- Residual Value % = 57% → Residual Value = 0.57 × $17,500 = $9,975
- Lease Term = 36 months
- Interest Rate (Money Factor) = 9% annually → Money Factor = 0.09 ÷ 24 = 0.00375
Step 1: Depreciation Fee
Depreciation Fee=(MSRP−Residual Value)Lease Term\text{Depreciation Fee} = \frac{(\text{MSRP} – \text{Residual Value})}{\text{Lease Term}} =(17,500−9,975)36=7,52536≈209.03= \frac{(17,500 – 9,975)}{36} = \frac{7,525}{36} \approx 209.03
Step 2: Finance Fee
Finance Fee=(MSRP+Residual Value)×Money Factor\text{Finance Fee} = (\text{MSRP} + \text{Residual Value}) \times \text{Money Factor} =(17,500+9,975)×0.00375=27,475×0.00375≈103.03= (17,500 + 9,975) \times 0.00375 = 27,475 \times 0.00375 \approx 103.03
Step 3: Monthly Lease Payment
Monthly Lease Payment=Depreciation Fee+Finance Fee\text{Monthly Lease Payment} = \text{Depreciation Fee} + \text{Finance Fee} =209.03+103.03=312.06= 209.03 + 103.03 = \boxed{312.06}
Final Answer:
Jennifer’s monthly lease payment is approximately $312.06.
Explanation (300+ Words):
When leasing a car, you’re essentially paying for the portion of the car’s value that you use over the lease term, along with interest charges. The monthly lease payment is mainly made up of two components: the depreciation fee and the finance (interest) fee.
The depreciation fee reflects the loss in the car’s value over the lease period. It’s calculated by subtracting the residual value (the car’s estimated value at the end of the lease) from the MSRP (or capitalized cost) and dividing it by the number of months in the lease. For Jennifer, the residual value is 57% of $17,500, which is $9,975. So, she’s responsible for the depreciation of $7,525 over 36 months.
The finance fee (also known as the rent charge) is the cost of borrowing the money to lease the vehicle. It’s based on the average value of the car during the lease, which is calculated by adding the MSRP and residual value and multiplying by the money factor. The money factor is derived from the annual interest rate divided by 24. In this case, 9% interest becomes a money factor of 0.00375.
Adding the depreciation fee of $209.03 and the finance fee of $103.03 gives a total monthly lease payment of $312.06. This payment structure allows Jennifer to drive the vehicle without having to purchase it outright while paying only for the value she uses during the lease. This approach is often chosen for flexibility, lower monthly costs, and access to newer vehicles more freque