## help_people 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.

1. help_people

@misty1212

2. whpalmer4

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

do you know how to read the table?

4. help_people

yes i do

5. help_people

@whpalmer4

6. help_people

i believe the answer is a?

7. whpalmer4

Why do you think the answer is A?

8. help_people

because

9. help_people

it just seems the best answer doesn't i believe it is a ( i do not think i would pick any other)

10. whpalmer4

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

11. whpalmer4

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

207 @whpalmer4

13. whpalmer4

good. how about after 2 years? 3? 4?

14. help_people

wait don't leave it is hard to get you back

15. help_people

214 221 and 228 @whpalmer4

16. whpalmer4

Okay, so let's do the same thing, except looking at the amount of money owed to Drake.

17. help_people

next time may you leave (asking this in the politess way possible)

18. whpalmer4

actually, before we do that, can you spot the pattern? How much would he owe after another year to Linda?

19. help_people

206, 212.12, 218.55, and 225.10

20. help_people

oh srry i will do that now

21. help_people

all harding by 7

22. help_people

23. whpalmer4

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

ok

25. help_people

what next

26. whpalmer4

Okay, can you see the pattern for the money owed to Drake? This is a bit harder to spot, perhaps.

27. help_people

+6

28. whpalmer4

Uh, if we are adding 6 each time, why doesn't it go 206, 212, 218, 224?

29. whpalmer4

How much gets added to the 206 to make the next amount?

30. help_people

?

31. help_people

i do not know with this one can you just tll me

32. whpalmer4

Do you know about compound interest?

33. help_people

no i do not

34. whpalmer4

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 ok so what do i do next ? 36. whpalmer4 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 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 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 may you please just show me i would understand it better 40. whpalmer4 Trust me, you understand better if you do it! Linda: $$200+7n$$ where $$n$$ is number of years 41. help_people ok so i will plug in 30 there and find my asnewr ? 42. help_people if what i said was correct i got 410 43. whpalmer4 well you'll find something that you need to know to answer, yes 44. help_people ? 45. help_people i got 410 46. whpalmer4 so, yes, after 30 years, he owes Linda 410. Is that twice 200? 47. help_people yes 48. help_people so a is correct? 49. whpalmer4 2*200 = 410? 50. help_people 400 51. whpalmer4 Right, so A is not correct, because he does not owe Linda twice the amount borrowed. 52. help_people he would owe linda more though so c 53. whpalmer4 how do you know that? Did you figure out the amount owed to linda after 30 years? 54. help_people 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 so is c right or not @whpalmer4 56. whpalmer4 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 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 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 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 ? 61. help_people please just tell me is the answer c or not @whpalmer4 62. whpalmer4 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 Do you have a calculator handy? 64. help_people yes 65. whpalmer4 do you know how to raise a number to a power with it? 66. help_people may this please not take 2 hours (again) :D 67. help_people exponetns? 68. whpalmer4 is there a $$y^x$$ button or something like that? 69. help_people i ws using google calc it was easier but let me get mine i will be 2 secs 70. whpalmer4 oh, no that is fine... you need to compute 200*(1.03)^30 71. help_people ok 72. whpalmer4 what do you get? 73. help_people 523999.1297299896 74. whpalmer4 hmm...didn't do that right. just try 1.03^30 first, then multiply it by 200 75. help_people 485.452494 and then a bunch of other numbers 76. whpalmer4 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

thank you so much :)

78. whpalmer4

you're welcome. I'll get anyone to the answer, if they are willing to work and learn :-)