Question

A real estate broker decides to lease a car for 36 months. Suppose the anual interest rate is 7.8%, the negotiated price is $49,000, there is no trade-in, and the down payment is $4,000. Find the monthly lease payment (in dollars). Assume that the residual value is 49% of the MSRP of $51,500. (Round your answer to the nearest cent.)

Answer 1

The monthly lease payment for the real estate broker's car is approximately 1,652.28.

Here's how to calculate the monthly lease payment for the real estate broker's car lease:

1. Determine the Principal Amount:

Subtract the down payment from the negotiated price: 49,000 (negotiated price) - 4,000 (down payment) = 45,000 (principal amount)

2. Calculate the Residual Value:

Multiply the MSRP by the residual value percentage: 51,500 (MSRP) x 49% = 25,235 (residual value)

3. Convert the Annual Interest Rate to Monthly:

Divide the annual interest rate by 12: 7.8% / 12 = 0.65% (monthly interest rate)

4. Apply the Lease Payment Formula:

Use the formula: Monthly payment =
`[(P - RV) * ((i(1 + i)^n) / ((1 + i)^n - 1))]`where:

P is the principal amount (45,000)

RV is the residual value (25,235)

i is the monthly interest rate (0.0065)

n is the lease term in months (36)

5. Calculate the Monthly Payment:

Plug the values into the formula:

Monthly payment = [(45,000 - 25,235) * (((0.0065)
`(1 + 0.0065)^36)`/
`((1 + 0.0065)^36`- 1))]

Monthly payment ≈ 1,652.28

Therefore, the monthly lease payment for the real estate broker's car is approximately 1,652.28.

Answer 2

To find the monthly lease payment, we need to use the formula:

Monthly lease payment = (Net capitalized cost - Residual value) / Lease term in months

where:

Net capitalized cost = negotiated price - down payment

Residual value = percentage of MSRP x MSRP

Lease term in months = 36

First, we need to calculate the net capitalized cost:

Net capitalized cost = $49,000 - $4,000 = $45,000

Next, we need to calculate the residual value:

Residual value = 49% x $51,500 = $25,235

Now we can plug in the values and solve for the monthly lease payment:

Monthly lease payment = ($45,000 - $25,235) / 36 = $548.76

Therefore, the monthly lease payment is approximately $548.76.