Question

Jonathan secured a 4-year car lease at 5.90% compounded annually that required him to make payments of $889.49 at the beginning of each month. Calculate the cost of the car if he made a downpayment of $2,000.

Round to the nearest cent

Answer 1

Ans: Cost of car = Down payment + Loan amount

= $ 2,000 + $ 37,948.81 (Loan amount from note1)

= $ 39,948.81

Note1:

Loan amount caluculation

PV = (P*(1-(1+r)-n ) / r

P = Monthly payment = $889.49

PV = Present Value = Loan amount =?

APR = 5.90 %

r = rate per period = APR/12 moths = 5.90%/12 = 0.004917

n = number of periods = 48 months (4years)

PV = (P*[1-(1+r)-n]) / r   

PV = ($ 889.49 * [1-(1+0.004917)-48 )/ 0.004917

PV = ($889.49*[1-(0.790238)] / 0.004917 ((1+0.004917)-48 = 0.790238

PV = ($889.49*[0.209762] )/0.004917

PV = $186.5816/0.004917

PV = $ 37,948.81