Question

# Lupé made a down payment of \$8000 toward the purchase of a new car. To pay...

Lupé made a down payment of \$8000 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 5%/year compounded monthly. Under the terms of her finance agreement she is required to make payments of \$440/month for 36 months.

What is the cash price of the car? (Round your answer to the nearest cent.)

 Mortgage amount = Presnt value of annuity of monthly payment Present Value of annuity = P*PVAF(rate,time) where P = monthly payment=\$440 t = time in months=36 months r = interest rate = r= 0.05/12=0.004167 calculation of PVAF(0.4167%,36) PVAF(rate,time) = [1-(1+r)^-n]/r PVAF(0.4167%,36) = [1-(1+0.004167)^-36]/0.004167 = [1-(1.004167)^-36]/0.004167 = [1-0.0.860966]/0.004167 = 0.139034/0.004167 = 33.3655 Present Value of annuity = \$440*33.3655 = \$    14,680.82 cash price of car = \$8,000+\$14,680.82 = \$    22,680.82 If you have any doubt,please ask Please upvote the answer