1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Lesechka [4]
3 years ago
13

I want to calculate APR for Automobile Loans without a calculator, but I struggle with division. Could someone please explain th

e process step by step?
Mathematics
1 answer:
vfiekz [6]3 years ago
6 0

Explanation:

Of all the variables in an amortization formula, the interest rate is the one that cannot be solved for. Finding APR for a given loan is generally an iterative process, or one that can be done by many spreadsheets, graphing calculators, and on-line tools.

The formula for the value of a monthly loan payment A on principal P, for t years, at interest rate r is ...

  A = P(r/12)/(1 -(1 +r/12)^(-12t))

but that is of no direct help in finding APR.

__

This formula can be used to develop relations that can approximate APR. The formulas below are for different loan lengths, and will be accurate to 2 decimal places of APR value for APRs in the range of 0 to 15%.

They work like this:

  Find the ratio of total loan repayment cost to the principal amount of the loan. (Division is required for this.) It will generally be a number between 1 and about 1.5 for auto loans of reasonable duration.

Use that value for x in the expression corresponding to the loan length. The range of output from these formulas is from 0 to 15, meaning the APR is 0% to 15%.

<em>APR Formulas</em>

<u>2-year loan</u>

  APR = ((((8.03501x - 53.6947)x + 153.636)x - 248.528)x + 306.753)x -166.201

<u>3-year loan</u>

  APR = ((((4.37626x - 30.7798)x + 92.6767)x - 157.555)x + 203.183)x -111.901

<u>4-year loan</u>

  APR = ((((2.7783x - 20.3207)x + 63.6117)x - 112.328)x + 150.19)x -83.9314

<u>5-year loan</u> (note the leading minus sign)

  APR = ((((( -1.28076x + 11.1732)x - 42.3671)x + 91.6612)x - 125.977)x + 137.601)x -70.8105

<u>6-year loan</u> (note the leading minus sign)

  APR = (((((-0.864078x + 7.82602)x - 30.8075)x + 69.1893)x - 98.6637)x + 111.919)x -58.599

<em>Example</em>

You want to borrow $22,175, and you're told that your monthly payment amount on a 4-year loan would be $512.99. Your total repayment is ...

  $512.99×48 = $24,623.52

Dividing this by the amount you borrowed, you get a ratio of ...

  24,623.52/22,175 ≈ 1.1104

Using this value in the formula for the 4-year loan APR, we make the following calculations:

   APR = ((((2.7783(1.1104) - 20.3207)(1.1104) + 63.6117)(1.1104) - 112.328)(1.1104) + 150.19)(1.1104) -83.9314

     = (((-17.2357)(1.1104) + 63.6117)(1.1104) - 112.328)(1.1104) + 150.19)(1.1104) -83.9314

     = (((44.4732)(1.1104) - 112.328)(1.1104) + 150.19)(1.1104) -83.9314

     = ((-62.945)(1.1104) + 150.19)(1.1104) -83.9314

     = (80.2959)(1.1104) -83.9314

     = 5.2292

  APR = 5.23 . . . percent (result should be rounded to 2 decimal places)

__

<em>Comment on formula evaluation</em>

It is tedious, but necessary, to keep 4 decimal places of precision in each of the intermediate calculations, rounding where required. These formulas are taking relatively small differences of relatively large numbers, so the best reasonable precision should be maintained in all calculations. The final answer should be rounded to 2 decimal places.

These computations can be done by hand, but a calculator or spreadsheet is immensely helpful.

You might be interested in
Hello, can you explain this topic im in 6th grade ​
Andrew [12]

Hello there I hope you are having a great day :)

<u>The Topic Shifting digits:</u>

Shifting digits - Putting a digit in a different place. For a example Take the number 358 you would exchange the number from the hundreds that would equal 838 this meaning that you what to make a bigger number than a small one.

Examples:

1. 358 equal 838

2. 204 equal 402

3. 188 equal 881

You are just making them smaller to a greater number :)

Hopefully that helps you :)

 

<u></u>

5 0
2 years ago
Read 2 more answers
sandra raised 15 dollars for pta and nita raised 45 dollars how many times as much money did nita raise as compared to sandra​
OlgaM077 [116]

Answer:

3 times (3x)

Step-by-step explanation:

Sandra raised 15 dollars.

Nita raised 45

45 divided by 15 is 3

3 * 15 = 45

7 0
2 years ago
If there were 75 students and 3/5 moved how many moved?
xeze [42]

Answer: 45

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
For EACH ordered pair, determine if its a solution to 2x+9y=13
vladimir1956 [14]
The answer is (2,1). 2*2=4 and 9*1=9. 9+4=13
8 0
3 years ago
What is the equation in slope intercept form for (2,5) (3,12)
kondaur [170]

Slope formula: y2-y1/x2-x1

= 12-5/3-2

= 7/1

= 7

_____

Best Regards,

Wolfyy :)

7 0
3 years ago
Other questions:
  • Do these ratios form a proportion? 26 medium hats to 2 small hats 39 medium hats to 3 small hats
    8·2 answers
  • If angle PDQ equals 23 degrees and angle SDQ equals 11 degrees what is angle PDS?
    8·1 answer
  • How to solve -3 1/2 + 5 4/5?
    14·1 answer
  • What is 25 % off $249
    5·2 answers
  • PLZ HELP ME IM TIMED YOU GUYS
    15·1 answer
  • If -11 + N = -11, then N is the _____.
    8·2 answers
  • :)will mark brainliest!!!
    7·1 answer
  • There are 625 students in Weaver Junior High School. Jimmy surveyed the 30 students in his English class regarding their favorit
    11·1 answer
  • Which of the following statements is true about the sequence? Select all that apply.
    9·1 answer
  • Can anyone do this i need it rn+ tell me the part when u answer
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!