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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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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the table got mangled in your posting. I think it looks like this: \[\begin{array}{lll} \text{Year} & \text{Linda} &\text{Drake}\\ 1 & 207 & 206 \\ 2 & 214 & 212.18 \\ 3 & 221 & 218.55 \\ 4 & 228 & 225.1 \\ \end{array}\]
do you know how to read the table?

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Other answers:

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

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