Princeton ..Interest on amount..pg no.177

[prachich1987]

If one of jean's credit cards charges more than 2 % interest each month on any balance,and this month Jean paid more than $17.85 in interest,what is the least possible amount of Jean's balance for this month?

1) $ 357.00
2) $ 357.50
3) $ 892.00
4) $ 892.50
5) $ 893.00

Source : Princeton
OA : later

[HPengineer]

2/(100)X = 17.85

2X = 1785

X = 892.5

If i am interpreting the question correctly they say MORE than 2% and MORE then 17.85 only value of the answer choices that is larger then balance of 892.5 which we calculated using the under bound values of 2% and 17.85 there fore i would mark choice E...

[Anurag@Gurome]

If one of jean's credit cards charges more than 2 % interest each month on any balance,and this month Jean paid more than $17.85 in interest,what is the least possible amount of Jean's balance for this month?

1) $ 357.00
2) $ 357.50
3) $ 892.00
4) $ 892.50
5) $ 893.00

Say the balance in Jean's card for that month is $x, interest rate is r% and interest for this month is $I.

Therefore, x*(r/100) = I => x = 100*(I/r)
Thus to minimize x, we have to minimize I and maximize r.

Now r > 2 and I > 17.85
Therefore minimum possible value of I is something just greater than 17.85 but maximum possible value of r can be anything greater than 2. Let us assume the minimum possible value of I be 17.85.

Thus, minimum possible x = 100*17.85/(Maximum possible r)
As we don't know the maximum possible value of r, we can not uniquely determine minimum possible value of x. Therefore the minimum possible value of x is the minimum value out of the options, i.e. 357.00.

Let's see if that holds.
x = 357.00 and I = 17.85 => r = 100*(I/x) = 100*(17.85/357.00) = 5 > 2
Now remember that we assumed I to be 17.85, but actually it is something just greater than 17.85. In that case also we can maintain x = 357.00 by taking a value of r which is also just greater than 5 and thus more than 2.

Thus our logic holds and least possible amount of Jean's balance for this month is whatever minimum amount is available to us.

he correct answer is A.

[prachich1987]

@ HpEngineer

Your answer matched with the OA, which is E
But according to me OA should be D.
As you have calculated above 2% on 892.50 will give us 17.85.
We know that the credit card charges more than 2%.
So 892.50*(rate more than 2%) will be definitely greater than 17.85
Hence D should be the answer.
Please tell me where I am going wrong.

@Anurag:

Thanks for your explanation.
But when I calculate 2% interest on 357,I get a value much lesser than 17.85.
if you could, plz advise what's wrong with HPEngineer's method.

[Anurag@Gurome]

@Anurag:

Thanks for your explanation.
But when I calculate 2% interest on 357,I get a value much lesser than 17.85.
if you could, plz advise what's wrong with HPEngineer's method.

Why should you do that?
Interest is not 2%. It is something more than 2%, which I calculated as something just greater than 5% for $357 balance.

Problem with HPEngineer's method:

• As I have shown in my solution, Balance = Interest/Interest Rate
  Now to minimize balance we have to minimize interest and maximize the interest rate. Now minimum interest and minimum interest rate are available but maximum interest rate is not. What HPEngineer has done is considered 2% as the interest rate (which is minimum interest rate) while calculating minimum balance. Now as interest rate is in the denominator, minimizing it maximizes the expression and thus maximizes balance.

Hope it is clear now.

Note: I think the question should read like the following for the OA to be true and also HPEngineers method

• If one of jean's credit cards charges less than 2% interest each month on any balance,and this month Jean paid more than $17.85 in interest,what is the least possible amount of Jean's balance for this month?

[HPengineer]

@ anurag

I see your point now... Technically we can take the smallest amount listed from answer choice and since intrest is greater then 2 it could for instance be 20% which would give us a value larger then 17.35 with the lowest balance listed.

Am i with you?


@prachich

Im not sure why the answer is E but by same logic anurag explained you are correct in saying D... Trully we should be taking the smallest value of the answer choice and maxing the intrest to see if it will give us something greater then 17.35

[Anurag@Gurome]

@ anurag

I see your point now... Technically we can take the smallest amount listed from answer choice and since intrest is greater then 2 it could for instance be 20% which would give us a value larger then 17.35 with the lowest balance listed.

Am i with you?

Correct!

[RACHVIK]

I would like to differ.

I think option E is the best choice here. For option A to work, interest rate has to be at least over 5% but option E will work whatever be the interest rate as long as it is over 2%. It satisfies both the criteria - Interest over $17.85 & ROI over 2%.