Question

Lupe made a down payment of $2200 toward the purchase of a new car. To pay the balance of the purchase price, she has secured a loan from her bank at the rate of 11%/year compounded monthly. Under the terms of her finance agreement she is required to make payments of $200/month for 48 months. What is the cash price of the car? (Round your answer to the nearest cent.)

Answer 1

Answer:

Cash price of the car

= Down payment + A(1 - (1+r/m)-nm

                                            r/m

= $2,200 + $200(1-(1+0.11/12)-4x12

                                  0.11/12

= $2,200 + $200(1-(1+0.0091666667)-48

                                0.0091666667

= $2,200 + $200(1-(1.009166666667)-48

                               0.0091666667

= $2,200 + `$200(38.691421)

= $9,938

Explanation:

The cash price of the car is equal to the down payment plus the present value of the monthly installment.  The present value of the monthly installment is obtained by using present value of annuity formula.