Question 976983: I AM SO LOST!!! Presvent value... future value... I am confused. Here is the problem:
Imagine that you have decided you need a new car, but not any car will do; you have decided to purchase the car of your dreams. Conduct some research as to the cost of this car. You have determined in this imagined scenario that you could afford to make a 10% down payment. You can borrow the balance either from your local bank using a four-year loan or from the dealership’s finance company. If you purchase from your dealership’s finance company, the APR will be 10% with your 10% down and monthly payments over three years. However, the dealership will give you a rebate of 5% of the car price after the three year term is complete. You want the best deal possible, so you consider the following questions:
• What type of car have you selected, and what will it cost?
• What is the interest rate from your local bank for a car loan for four years?
• What will your payment be to your local bank, assuming your 10% down payment? Be sure to use the formula provided in Chapter 4 and show your work. How much will that car have cost in four years?
• What will your payment be to the dealership finance company assuming your 10% down payment? Be sure to use the formula provided in Chapter 4 and show your work. How much will that car have cost in 3 years?
• Which is the better deal and why?
Now my vehicle cost $59,500 and my bank has a rate of 4%. What do I do for each part?
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! • What type of car have you selected, and what will it cost?
You selected a car that costs $59,500.
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• What is the interest rate from your local bank for a car loan for four years?
You stated 4%
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• What will your payment be to your local bank, assuming your 10% down payment? Be sure to use the formula provided in Chapter 4 and show your work. How much will that car have cost in four years?
down payment = 10% of $59,500 = 0.10*59500 = 5,950
I don't know the book you have, so I don't know the exact formula you are using. There are slightly different variations. The formula I'm used to is
M = monthly payment
L = loan amount
i = monthly interest rate
n = number of months
The good news is that it doesn't matter since all of the formulas are the same. Just written in different ways.
In this case, you pay 10% down, so you have to pay off 90% of the car value. 90% of $59,500 = 0.90*59500 = 53,550. Therefore, you need to pay off the remaining $53,550. This is amount loaned to you.
L = 53,550
The monthly interest rate is the annual rate divided by 12.
(annual rate)/12 = (4%)/12 = (1/3)% = (0.33333)%
Convert (0.33333)% to decimal form
(0.33333)% = (0.33333)/100 = 0.0033333
This decimal number is approximate because the 3's technically go on forever
So, i = 0.0033333
The number of months is (4 years)*(12 months per year) = 48 months
n = 48
Summary so far:
L = 53,550
i = 0.0033333
n = 48
Plug these values into the formula I gave you above
 Plug in the given summary values above
 Use a calculator here (note: hit the equals sign to have it compute the result)
 Round to the nearest penny (ie nearest hundredth)
The monthly payment is $1,209.11
Multiply this by the number of months (48) to get 48*1209.11 = 58,037.28
The value 58,037.28 represents the total amount paid back. Add on the down payment to get 58,037.28 + 5,950 = 63,987.28
So the total cost of the car is $63,987.28 (if you go with the bank option)
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• What will your payment be to the dealership finance company assuming your 10% down payment? Be sure to use the formula provided in Chapter 4 and show your work. How much will that car have cost in 3 years?
Use the same formula. L will be the same since the same amount is loaned to you. The i value will be different since the dealership uses a different interest rate
i = (10%)/12 = (0.10)/12 = 0.00833333 (approximate)
The n will be different since it's 3 years instead of 4.
n = 3*12 = 36 months
Summary:
L = 53,550
i = 0.00833333
n = 36
 Plug in the given summary values above
 Use a calculator here (note: hit the equals sign to have it compute the result)
 Round to the nearest penny (ie nearest hundredth)
Total Amount Paid Back = (number of months)*(monthly payment) = 36*1727.91 = 62,204.76
Rebate = 5% of car price = 5% of $59,500 = 0.05*59500 = 2,975
Total Cost = (down payment) + (amount paid back) - (Rebate) = 5,950 + 62,204.76 - 2,975 = 65,179.76
Total Cost = $65,179.76
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• Which is the better deal and why?
Comparison of the two plans
| Monthly Payment | Total Cost of Car | | Bank | $1,209.11 | $63,987.28 | | Dealership | $1,727.91 | $65,179.76 |
So with the dealership plan, you are paying more per month (1727.91-1209.11 = 518.8 more per month) and the total cost of the car is higher (65,179.76 - 63,987.28 = 1,192.48 dollars higher).
The rebate of 5% did not do enough to lower the total cost. Even if it did, the rebate usually takes time to get back to the customer, so you have to factor in that amount of time that you don't have that rebate money in your pocket.
Ultimately, the bank loan is the better option. It has a lower monthly payment and lower total cost.
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Jim
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