Final answer:
To calculate the monthly lease payments, use the formula for an annuity which incorporates the vehicle's purchase price, residual value, interest rate, and lease term. The monthly payment is the sum of depreciation and finance charge components.
Step-by-step explanation:
Calculating the Monthly Lease Payments
To calculate the monthly lease payments for a 36-month lease on a car with a purchase price of $30,000, a residual value of $15,000, and an annual interest rate of 6% compounded monthly, we can use the formula for an annuity. The lease payments rely on the depreciation amount, which is the difference between the purchase price and the residual value, and the finance charge, which is based on the interest rate. The formula for the monthly payment (M) is:
M = (P - R) / ((1 - (1 + i)^{-n}) / i) + (P + R) * (i / 2),
where P is the purchase price, R is the residual value, i is the monthly interest rate (APR/12), and n is the number of monthly payments.
Plugging in the values:
P = $30,000
R = $15,000
APR = 6% per year or 0.06
i = 0.06 / 12 = 0.005 per month
n = 36 months
First, calculate the depreciation and finance charge components separately:
Depreciation component = ($30,000 - $15,000) / ((1 - (1 + 0.005)^{-36}) / 0.005)
Finance charge component = ($30,000 + $15,000) * (0.005 / 2)
Finally, add the two components to find the monthly lease payment:
Depreciation component + Finance charge component = Monthly lease payment.
Once you calculate the depreciation and finance charge components and sum them up, you will find the monthly payment required for the lease.