Final answer:
To determine the cost of the car, calculate the present value of the lease payments as an annuity due and add the downpayment. The lease terms dictate the monthly payment, interest rate, and lease duration. Apply the formula for present value of an annuity due to find the cost before adding the downpayment amount.
Step-by-step explanation:
The question asks to calculate the cost of a car with a 6-year lease, an annual interest rate of 5.90% compounded annually, and monthly payments of $884.30, including a down payment of $3,250.
To solve this, we need the present value (PV) of the annuity, which represents the total cost of the car lease including interest but excluding the downpayment.
Since payments are made at the beginning of the month, we use the formula for the present value of an annuity due:
PV = Pmt × × (1 - (1 + r)^{-n}) / r
Where:
Pmt is the payment amount per period ($884.30)
r is the monthly interest rate (5.90% per year / 12 months)
n is the total number of payments (6 years × 12 months/year)
We calculate the present value and then add the down payment to find the total cost of the car.