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  • one year ago

Bill borrowed the same amount of money from Linda and Drake. The table below shows the amount, in dollars, that Bill would owe them after different numbers of years: Year 1 2 3 4 Linda 207 214 221 228 Drake 206 212.18 218.55 225.10 Which statement is true about the money Bill would owe Linda and Drake after 30 years? He would owe Linda twice the amount he borrowed. He would owe both the same amount of money. He would owe Linda more money. He would owe Drake more money.

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  1. help_people
    • one year ago
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    @misty1212

  2. whpalmer4
    • one year ago
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    the table got mangled in your posting. I think it looks like this: \[\begin{array}{lll} \text{Year} & \text{Linda} &\text{Drake}\\ 1 & 207 & 206 \\ 2 & 214 & 212.18 \\ 3 & 221 & 218.55 \\ 4 & 228 & 225.1 \\ \end{array}\]

  3. whpalmer4
    • one year ago
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    do you know how to read the table?

  4. help_people
    • one year ago
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    yes i do

  5. help_people
    • one year ago
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    @whpalmer4

  6. help_people
    • one year ago
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    i believe the answer is a?

  7. whpalmer4
    • one year ago
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    Why do you think the answer is A?

  8. help_people
    • one year ago
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    because

  9. help_people
    • one year ago
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    it just seems the best answer doesn't i believe it is a ( i do not think i would pick any other)

  10. whpalmer4
    • one year ago
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    That's not convincing :-) Let's work on your table reading skills. In year 1, how much does Bill owe Linda?

  11. whpalmer4
    • one year ago
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    Look at the line with 1 in the first column. Now read straight across in that row until you get to the column which has Linda at the top. What is the value there? That is the amount that Bill owes Linda after 1 year.

  12. help_people
    • one year ago
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    207 @whpalmer4

  13. whpalmer4
    • one year ago
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    good. how about after 2 years? 3? 4?

  14. help_people
    • one year ago
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    wait don't leave it is hard to get you back

  15. help_people
    • one year ago
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    214 221 and 228 @whpalmer4

  16. whpalmer4
    • one year ago
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    Okay, so let's do the same thing, except looking at the amount of money owed to Drake.

  17. help_people
    • one year ago
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    next time may you leave (asking this in the politess way possible)

  18. whpalmer4
    • one year ago
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    actually, before we do that, can you spot the pattern? How much would he owe after another year to Linda?

  19. help_people
    • one year ago
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    206, 212.12, 218.55, and 225.10

  20. help_people
    • one year ago
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    oh srry i will do that now

  21. help_people
    • one year ago
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    all harding by 7

  22. help_people
    • one year ago
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    *adding

  23. whpalmer4
    • one year ago
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    Very good. So if we use \(n\) as the year number, we could write the amount owed to Linda in year \(n\) as \[200+7n\]right? When we start, (year \(0\)) he owes her \(200\), after 1 year, \(200+7(1) = 207\) etc.

  24. help_people
    • one year ago
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    ok

  25. help_people
    • one year ago
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    what next

  26. whpalmer4
    • one year ago
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    Okay, can you see the pattern for the money owed to Drake? This is a bit harder to spot, perhaps.

  27. help_people
    • one year ago
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    +6

  28. whpalmer4
    • one year ago
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    Uh, if we are adding 6 each time, why doesn't it go 206, 212, 218, 224?

  29. whpalmer4
    • one year ago
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    How much gets added to the 206 to make the next amount?

  30. help_people
    • one year ago
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    ?

  31. help_people
    • one year ago
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    i do not know with this one can you just tll me

  32. whpalmer4
    • one year ago
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    Do you know about compound interest?

  33. help_people
    • one year ago
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    no i do not

  34. whpalmer4
    • one year ago
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    My first guess looking at the table is that it is compound interest for Drake, and simple interest for Linda, because Linda's column increases by the same amount each year, and Drake's increases by a slightly larger amount each year. Simple interest means that you multiply the interest rate by the initial balance and add that amount each period (here, 1 year). As Linda's amount goes up by $7 each year, Linda's interest rate (\(i_{L}\)) must be such that \[$7 = $200*i_{L}\] And if you do the math, that turns out to be 3.5%.

  35. help_people
    • one year ago
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    ok so what do i do next ?

  36. whpalmer4
    • one year ago
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    Now, compound interest means that each period (again, a year here), you figure the interest not just on the initial balance, but also on all the interest so far. Drake: 200, 206, 212.18, 225.10 So the first year, compound and simple interest are the same: \[$6 = $200*i_D\]and that means that the interest rate is 3%. However, the second year, the interest is\[$206*i_D = $206*0.03 = $6.18\] the third year, the interest is \[212.18*0.03 = $6.37\] etc. See how the amount of interest gets larger?

  37. whpalmer4
    • one year ago
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    I skipped a year in my list, should have been 200, 206, 212.18, 218.55, 225.10 So, we can write this in formula form as \[200(1+i_D)^n\]where \(n\) is the number of years, and \(i_D\) is the interest rate per year, expressed as a decimal (so \(3\% = 0.03\))

  38. whpalmer4
    • one year ago
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    Now to answer the question. Question asks about what the balances will be after 30 years. Using the formula from before, what is the balance for Linda after 30 years?

  39. help_people
    • one year ago
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    may you please just show me i would understand it better

  40. whpalmer4
    • one year ago
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    Trust me, you understand better if you do it! Linda: \(200+7n\) where \(n\) is number of years

  41. help_people
    • one year ago
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    ok so i will plug in 30 there and find my asnewr ?

  42. help_people
    • one year ago
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    if what i said was correct i got 410

  43. whpalmer4
    • one year ago
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    well you'll find something that you need to know to answer, yes

  44. help_people
    • one year ago
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    ?

  45. help_people
    • one year ago
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    i got 410

  46. whpalmer4
    • one year ago
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    so, yes, after 30 years, he owes Linda 410. Is that twice 200?

  47. help_people
    • one year ago
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    yes

  48. help_people
    • one year ago
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    so a is correct?

  49. whpalmer4
    • one year ago
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    2*200 = 410?

  50. help_people
    • one year ago
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    400

  51. whpalmer4
    • one year ago
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    Right, so A is not correct, because he does not owe Linda twice the amount borrowed.

  52. help_people
    • one year ago
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    he would owe linda more though so c

  53. whpalmer4
    • one year ago
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    how do you know that? Did you figure out the amount owed to linda after 30 years?

  54. help_people
    • one year ago
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    please you know it is c just tell me that it is c we have been here for 2 HOURS am i right or not?

  55. help_people
    • one year ago
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    so is c right or not @whpalmer4

  56. whpalmer4
    • one year ago
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    look, I've given you the tools to determine the answer, and some of the questions you should be asking. if you aren't interested, just pick one and move on. I'm not sure why you kids think that being told an answer is going to do anything besides get 1 question correct if you don't actually learn anything.

  57. help_people
    • one year ago
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    i have learned just every time i say an answer you are like nope thats not it or even if its right you can't just say yes please tell me if it is right can you have some decency we ahem been here for 2 HOURS and i would really appreciate if you could tell me the answer because 2 HOURS OF WORK would be wasted @whpalmer4

  58. whpalmer4
    • one year ago
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    I told you how to compute the amount owed to Linda, and how to compute the amount owed to Drake. If you compute both of those amounts, you can determine the answer without guessing, and KNOW whether or not it is correct. You should not need me or anyone else to tell you if C is right or not.

  59. whpalmer4
    • one year ago
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    If you don't know how to solve the problem, then you won't be able to have any confidence that the answer provided by some random person who says "the answer is <whatever>" is correct.

  60. help_people
    • one year ago
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    ?

  61. help_people
    • one year ago
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    please just tell me is the answer c or not @whpalmer4

  62. whpalmer4
    • one year ago
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    from the OpenStudy code of conduct: Give Help, Not Answers I will encourage and guide those needing help, and not just give them an answer

  63. whpalmer4
    • one year ago
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    Do you have a calculator handy?

  64. help_people
    • one year ago
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    yes

  65. whpalmer4
    • one year ago
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    do you know how to raise a number to a power with it?

  66. help_people
    • one year ago
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    may this please not take 2 hours (again) :D

  67. help_people
    • one year ago
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    exponetns?

  68. whpalmer4
    • one year ago
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    is there a \(y^x\) button or something like that?

  69. help_people
    • one year ago
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    i ws using google calc it was easier but let me get mine i will be 2 secs

  70. whpalmer4
    • one year ago
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    oh, no that is fine... you need to compute 200*(1.03)^30

  71. help_people
    • one year ago
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    ok

  72. whpalmer4
    • one year ago
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    what do you get?

  73. help_people
    • one year ago
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    523999.1297299896

  74. whpalmer4
    • one year ago
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    hmm...didn't do that right. just try 1.03^30 first, then multiply it by 200

  75. help_people
    • one year ago
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    485.452494 and then a bunch of other numbers

  76. whpalmer4
    • one year ago
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    okay, that's correct. after 30 years, Bill owes Drake $485.45, which is more than he owes Linda. I wasn't willing to just tell you that, because depending on the number of years and the interest rate, he owes more to Linda. It actually takes about 11 years before the compounding of the lower interest rate he pays to Drake catches up to the higher simple interest rate paid to Linda. In my opinion, that is the entire point of this problem, so just telling you "yeah, it's C" when you make a guess defeats any purpose in helping you, and that would mean that I wasted the time.

  77. help_people
    • one year ago
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    thank you so much :)

  78. whpalmer4
    • one year ago
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    you're welcome. I'll get anyone to the answer, if they are willing to work and learn :-)

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