help_people
  • help_people
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.
Mathematics
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
help_people
  • help_people
@misty1212
whpalmer4
  • whpalmer4
the table got mangled in your posting. I think it looks like this: \[\begin{array}{lll} \text{Year} & \text{Linda} &\text{Drake}\\ 1 & 207 & 206 \\ 2 & 214 & 212.18 \\ 3 & 221 & 218.55 \\ 4 & 228 & 225.1 \\ \end{array}\]
whpalmer4
  • whpalmer4
do you know how to read the table?

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More answers

help_people
  • help_people
yes i do
help_people
  • help_people
@whpalmer4
help_people
  • help_people
i believe the answer is a?
whpalmer4
  • whpalmer4
Why do you think the answer is A?
help_people
  • help_people
because
help_people
  • help_people
it just seems the best answer doesn't i believe it is a ( i do not think i would pick any other)
whpalmer4
  • whpalmer4
That's not convincing :-) Let's work on your table reading skills. In year 1, how much does Bill owe Linda?
whpalmer4
  • 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.
help_people
  • help_people
207 @whpalmer4
whpalmer4
  • whpalmer4
good. how about after 2 years? 3? 4?
help_people
  • help_people
wait don't leave it is hard to get you back
help_people
  • help_people
214 221 and 228 @whpalmer4
whpalmer4
  • whpalmer4
Okay, so let's do the same thing, except looking at the amount of money owed to Drake.
help_people
  • help_people
next time may you leave (asking this in the politess way possible)
whpalmer4
  • whpalmer4
actually, before we do that, can you spot the pattern? How much would he owe after another year to Linda?
help_people
  • help_people
206, 212.12, 218.55, and 225.10
help_people
  • help_people
oh srry i will do that now
help_people
  • help_people
all harding by 7
help_people
  • help_people
*adding
whpalmer4
  • 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.
help_people
  • help_people
ok
help_people
  • help_people
what next
whpalmer4
  • whpalmer4
Okay, can you see the pattern for the money owed to Drake? This is a bit harder to spot, perhaps.
help_people
  • help_people
+6
whpalmer4
  • whpalmer4
Uh, if we are adding 6 each time, why doesn't it go 206, 212, 218, 224?
whpalmer4
  • whpalmer4
How much gets added to the 206 to make the next amount?
help_people
  • help_people
?
help_people
  • help_people
i do not know with this one can you just tll me
whpalmer4
  • whpalmer4
Do you know about compound interest?
help_people
  • help_people
no i do not
whpalmer4
  • 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%.
help_people
  • help_people
ok so what do i do next ?
whpalmer4
  • 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?
whpalmer4
  • 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 \(3\% = 0.03\))
whpalmer4
  • 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?
help_people
  • help_people
may you please just show me i would understand it better
whpalmer4
  • whpalmer4
Trust me, you understand better if you do it! Linda: \(200+7n\) where \(n\) is number of years
help_people
  • help_people
ok so i will plug in 30 there and find my asnewr ?
help_people
  • help_people
if what i said was correct i got 410
whpalmer4
  • whpalmer4
well you'll find something that you need to know to answer, yes
help_people
  • help_people
?
help_people
  • help_people
i got 410
whpalmer4
  • whpalmer4
so, yes, after 30 years, he owes Linda 410. Is that twice 200?
help_people
  • help_people
yes
help_people
  • help_people
so a is correct?
whpalmer4
  • whpalmer4
2*200 = 410?
help_people
  • help_people
400
whpalmer4
  • whpalmer4
Right, so A is not correct, because he does not owe Linda twice the amount borrowed.
help_people
  • help_people
he would owe linda more though so c
whpalmer4
  • whpalmer4
how do you know that? Did you figure out the amount owed to linda after 30 years?
help_people
  • 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?
help_people
  • help_people
so is c right or not @whpalmer4
whpalmer4
  • 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.
help_people
  • 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
whpalmer4
  • 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.
whpalmer4
  • 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 " is correct.
help_people
  • help_people
?
help_people
  • help_people
please just tell me is the answer c or not @whpalmer4
whpalmer4
  • 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
whpalmer4
  • whpalmer4
Do you have a calculator handy?
help_people
  • help_people
yes
whpalmer4
  • whpalmer4
do you know how to raise a number to a power with it?
help_people
  • help_people
may this please not take 2 hours (again) :D
help_people
  • help_people
exponetns?
whpalmer4
  • whpalmer4
is there a \(y^x\) button or something like that?
help_people
  • help_people
i ws using google calc it was easier but let me get mine i will be 2 secs
whpalmer4
  • whpalmer4
oh, no that is fine... you need to compute 200*(1.03)^30
help_people
  • help_people
ok
whpalmer4
  • whpalmer4
what do you get?
help_people
  • help_people
whpalmer4
  • whpalmer4
hmm...didn't do that right. just try 1.03^30 first, then multiply it by 200
help_people
  • help_people
485.452494 and then a bunch of other numbers
whpalmer4
  • 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.
help_people
  • help_people
thank you so much :)
whpalmer4
  • whpalmer4
you're welcome. I'll get anyone to the answer, if they are willing to work and learn :-)

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