Question 976983
<font color="blue">•	What type of car have you selected, and what will it cost?</font>


You selected a car that costs $59,500.


--------------------------------------------------------------------------------------------------------------

<font color="blue">•	What is the interest rate from your local bank for a car loan for four years? </font>


You stated 4%


--------------------------------------------------------------------------------------------------------------

<font color="blue">•	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? </font>


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 <i>exact</i> formula you are using. There are slightly different variations. The formula I'm used to is


{{{M = (L*i)/(1-(1+i)^(-n))}}}


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


{{{M = (L*i)/(1-(1+i)^(-n))}}}


{{{M = (53550*0.0033333)/(1-(1+0.0033333)^(-48))}}} Plug in the given summary values above


{{{M = 1209.10741754858}}} Use a <a href="http://web2.0calc.com/#(53550*0.0033333)/(1-(1+0.0033333)^(-48))">calculator</a> here (note: hit the equals sign to have it compute the result)


{{{M = 1209.11}}} 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)

--------------------------------------------------------------------------------------------------------------

<font color="blue">•	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? </font>


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


{{{M = (L*i)/(1-(1+i)^(-n))}}}


{{{M = (53550*0.00833333)/(1-(1+0.00833333)^(-36))}}} Plug in the given summary values above


{{{M = 1727.90777366433}}} Use a <a href="http://web2.0calc.com/#(53550*0.00833333)/(1-(1+0.00833333)^(-36))">calculator</a> here (note: hit the equals sign to have it compute the result)


{{{M = 1727.91}}} 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


--------------------------------------------------------------------------------------------------------------

<font color="blue">•	Which is the better deal and why? </font>


Comparison of the two plans


<table border=1><tr><td></td><td>Monthly Payment</td><td>Total Cost of Car</td></tr><tr><td>Bank</td><td>$1,209.11</td><td>$63,987.28</td></tr><tr><td>Dealership</td><td>$1,727.91</td><td>$65,179.76</td></tr></table>


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.



------------------------------------------------------------------------------------------------------------------------


If you need more one-on-one help, email me at <a href="mailto:jim_thompson5910@hotmail.com?Subject=I%20Need%20Algebra%20Help">jim_thompson5910@hotmail.com</a>. You can ask me a few more questions for free, but afterwards, I would charge you ($2 a problem to have steps shown or $1 a problem for answer only).


Alternatively, please consider visiting my website: <a href="http://www.freewebs.com/jimthompson5910/home.html">http://www.freewebs.com/jimthompson5910/home.html</a> and making a donation. Any amount is greatly appreciated as it helps me a lot. This donation is to support free tutoring. Thank you.


Jim

------------------------------------------------------------------------------------------------------------------------