Question

Jacob secured a 5-year car lease at 5.60% compounded annually that required her to make payments of $883.35 at the beginning of each month. Calculate the cost of the car if she made a downpayment of $1,500.

Answer 1

The cost of the car that Jacob leased is calculated by determining the present value of the annuity payments and adding the downpayment. Payments are managed as an annuity due, and adjustments are made to the annual interest rate to fit the monthly payment schedule.

Step-by-step explanation:

The cost of the car leased by Jacob can be calculated by finding the present value (PV) of the annuity payments she makes at the beginning of each month, plus the downpayment. Since payments are made at the beginning of the period, this is an annuity due. The formula for the present value of an annuity due is PV = PMT * [(1 - (1 + r)^-n) / r] * (1 + r), where PMT is the monthly payment, r is the monthly interest rate, and n is the total number of payments.

To calculate the cost of the car, we need to adjust the given annual interest rate to a monthly rate by dividing by 12. The formula becomes PV = 883.35 * [(1 - (1 + 0.056/12)^(-5*12)) / (0.056/12)] * (1 + 0.056/12). Once PV is calculated, we add the downpayment of $1,500 to find the total cost of the car.