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.

- help_people

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- help_people

@misty1212

- 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

do you know how to read the table?

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## More answers

- help_people

yes i do

- help_people

@whpalmer4

- help_people

i believe the answer is a?

- whpalmer4

Why do you think the answer is A?

- help_people

because

- 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

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

- 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

207 @whpalmer4

- whpalmer4

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

- help_people

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

- help_people

214 221 and 228 @whpalmer4

- whpalmer4

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

- help_people

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

- whpalmer4

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

- help_people

206, 212.12, 218.55, and 225.10

- help_people

oh srry i will do that now

- help_people

all harding by 7

- help_people

*adding

- 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

ok

- help_people

what next

- whpalmer4

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

- help_people

+6

- whpalmer4

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

- whpalmer4

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

- help_people

?

- help_people

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

- whpalmer4

Do you know about compound interest?

- help_people

no i do not

- 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

ok so what do i do next ?

- 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

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

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

may you please just show me i would understand it better

- whpalmer4

Trust me, you understand better if you do it!
Linda: \(200+7n\) where \(n\) is number of years

- help_people

ok so i will plug in 30 there and find my asnewr ?

- help_people

if what i said was correct i got 410

- whpalmer4

well you'll find something that you need to know to answer, yes

- help_people

?

- help_people

i got 410

- whpalmer4

so, yes, after 30 years, he owes Linda 410. Is that twice 200?

- help_people

yes

- help_people

so a is correct?

- whpalmer4

2*200 = 410?

- help_people

400

- whpalmer4

Right, so A is not correct, because he does not owe Linda twice the amount borrowed.

- help_people

he would owe linda more though so c

- whpalmer4

how do you know that? Did you figure out the amount owed to linda after 30 years?

- 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

so is c right or not @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

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

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

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

please just tell me is the answer c or not @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

Do you have a calculator handy?

- help_people

yes

- whpalmer4

do you know how to raise a number to a power with it?

- help_people

may this please not take 2 hours (again) :D

- help_people

exponetns?

- whpalmer4

is there a \(y^x\) button or something like that?

- help_people

i ws using google calc it was easier but let me get mine i will be 2 secs

- whpalmer4

oh, no that is fine...
you need to compute 200*(1.03)^30

- help_people

ok

- whpalmer4

what do you get?

- help_people

523999.1297299896

- whpalmer4

hmm...didn't do that right. just try 1.03^30 first, then multiply it by 200

- help_people

485.452494 and then a bunch of other numbers

- 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

thank you so much :)

- whpalmer4

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

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