math: precalc

posted by .

You are going to buy a $18,000 car. The dealer offers you $2000 cash back of nothing down and 0% financing for 60 months. If you take the financing, starting in one month you will pay one-sixtieth of $18,000 each month for 60 months. In some sense that is not really "0% financing" because you could have bought the care for, effectively, $16,000 and you will be making $18,000 in payments. Use the present value formula to determine the actual finance rate. [Hint: Do not expect to solve it algebraically.]

Present value Formula: A={R[1-(1+i)^-n]} / i

where A is the present value, R is the amount of each payment, i is the rate per time period, and n is the time period.

  • math: precalc -

    Please respond somebody!!!

  • math: precalc -

    16000 = 300(1 - (1+i)^-60)/i
    53.3333 = (1 - (1+i)^-60)/i

    After a few trial-and-error attempts with my calculator, I "sandwiched" the rate i between .004 and .0038

    so
    .004 53.24886
    i 53.33333
    .0038 53.561
    we can now set up an interpolation ratio
    (i - .004)/(.0038 - .004) = (53.3333-53.24886)/(53.561-53.24886)
    i = .003946

    check:
    300(1 - (1.003946)^-60)/.003946 = 15999.86
    not bad

    so the annual rate is approx .003946 x 12 = .04735
    or 4.735%

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. 12th grade economics

    Frank wants to buy a $10,000 car. The car dealer offers him financing of 60 payments at 9% interest. What will his payments be assuming he pays $0 down?
  2. math

    A car dealer will sell you the $16,450 car of your dreams for $3,260 down and payments of $339.97 per month for 48 months. What is the total amount paid for both car and financing?
  3. Math

    You want to purchase an automobile for $21,600. The dealer offers you 0% financing for 48 months or a $3,000 rebate. You can obtain 4.8% financing for 48 months at the local bank. Which option should you choose and why?
  4. math

    Debbie Snyder has just graduated from college and needs to buy a car to commute to work. She estimates that she can afford to pay about $ 450 per month for a loan or lease and has about $ 2,000 in savings to use for a down payment. …
  5. Finite Math

    The price of a new car is $24,000. Assume that an individual makes a down payment of 25% toward the purchase of the car and secures financing for the balance at the rate of 10%/year compounded monthly. (Round your answers to the nearest …
  6. Finance

    Debbie Snyder has just graduated from college and needs to buy a car to commute to work. She estimates that she can afford to pay about $ 450 per month for a loan or lease and has about $ 2,000 in savings to use for a down payment. …
  7. Finance

    You are interested in a new Ford Taurus. After visiting your Ford dealer, doing your research on the best leases available, you have three options. (i) Purchase the car for cash and receive a $1,900 cash rebate from Dealer A. The price …
  8. Finance

    You are interested in a new Ford Taurus. After visiting your Ford dealer, doing your research on the best leases available, you have three options. (i) Purchase the car for cash and receive a $1,900 cash rebate from Dealer A. The price …
  9. finance

    You have only saved 2,000. You are going to trade in your old car and get a new one. The dealership has offered you 3,000 for your trade, and you have accepted their offer. The car you want to buy costs 23,000 but you talked them down …
  10. finance

    You want to purchase a car. It costs 25,000. You have 3,000 that you have saved up for a down payment. You can go with the 5 year car and 60 month car loan. The car manufacture is offering a special deal on your car. You can get zero …

More Similar Questions