Lesson: Simple Interest and Compound Interest

Comment on Simple Interest and Compound Interest

in this above question how did u get the value of c=12
greenlight-admin's picture

c = the # of times the interest is compounded each year.
The question tells us that interest is compounded every month.
Since there are 12 months in a year, we know that the interest is compounded 12 times each year

Could you possibly give a detailed explanation of the answer for the GRE 3rd edition practice question on 262(13). I can't seem to calculate the answer correctly. Thank you.
greenlight-admin's picture

You bet.

Here's the question:

Pat invested a total of $3000 dollars. Part of the money was invested in a money market account that paid 10% SIMPLE annual interest, and the remainder of the money was invested in a fund that paid 8% SIMPLE annual interest. If the TOTAL interest earned at the end of the first year from these investments was $256, how much did Pat invest at 10% and how much at 8%?

Let x = amount invested at 10% interest
So, 3000-x = amount invested at 8% interest (since the two investments, when combined, must add to $3000)

So, the annual interest for the 10% investment = 0.1x
The annual interest for the 8% investment = 0.08(3000 - x)

The TOTAL interest earned is $256, so...
We can write: 0.1x + 0.08(3000 - x) = 256
Expand: 0.1x + 240 - 0.08x = 256
Simplify left side: 0.02x + 240 = 256
Subtract 240 from both sides: 0.02x = 16
Solve: x = 800

So, $800 was invested at 10% and the remaining $2200 was invested at 8%

Thank you!!

Shouldn't the formula be 1.1x = 1.08x(3000 - x) = 256?
greenlight-admin's picture

The question focuses solely on the total INTEREST that accumulates.

Your equation focuses on the total value of the investments (i.e., it represents the interest PLUS the initial investment.

For example, 0.1x represents the INTEREST that accumulates on x dollars at 10% interest.
Conversely, 1.1x represents the TOTAL VALUE of the investment of x dollars with 10% interest added to it.

Does that help?

Yes, thank you. I really appreciate your all your clarifications.

Hi, How did you solve questions on page 264(11) on the official guide 3rd edition?
greenlight-admin's picture

Hi Shukameli,

In the future, please transcribe the question.

The question is as follows: Kathleen's weekly salary was increased by 8 percent to $712.80. What was her weekly salary before the increase?

Let x = Kathleen's weekly salary BEFORE the increase
8% = 0.08
So, 8% of x = 0.08x

So, if we take her weekly salary BEFORE the increase (x) and increase it by 8%, we are adding an additional 0.08x to her salary to get a new salary of $712.80

We can write: x + 0.08x = $712.80
Simplify: 1.08x = $712.80
Solve: x = $712.80/1.08 = $660

NOTE: in general, if we want to increase a value by 8%, we just multiply the value by 1.08.
Likewise, if we want to increase a value by 13%, we multiply the value by 1.13.
If we want to increase a value by 38%, we multiply the value by 1.38.
and so on.

Does that help?

Cheers,
Brent

https://greprepclub.com/forum/the-number-0-is-between-the-two-nonzero-numbers-r-and-t-on-t-11601.html
This questions doesn't have anything to do with this section but i just wanted to know what section to find these question types.

Thank You
greenlight-admin's picture

Question link: https://greprepclub.com/forum/the-number-0-is-between-the-two-nonzero-nu...

As with many math questions, this question tests two different concepts:
1) Number line
2) Rules regarding products of positive/negative numbers

Given this, I would place this question under the following video: https://www.greenlighttestprep.com/module/gre-arithmetic/video/1059

https://greprepclub.com/forum/steve-s-property-tax-is-140-less-than-patricia-s-property-t-8154.html
What section would I find these types if question and lessons?

Thank You
greenlight-admin's picture

Question link: https://greprepclub.com/forum/steve-s-property-tax-is-140-less-than-patr...

This is definitely at percent question.

It would fit as a "percent increase/decrease" question here: https://www.greenlighttestprep.com/module/gre-arithmetic/video/1083
It would also fit as a regular percent question here: https://www.greenlighttestprep.com/module/gre-arithmetic/video/1078

I should also mention, that in my solution (https://greprepclub.com/forum/steve-s-property-tax-is-140-less-than-patr...), I use a nice fraction property to quickly convert $140/$2000+ into an approximate percent.
That fraction property occurs here: https://www.greenlighttestprep.com/module/gre-arithmetic/video/1067

Cheers,
Brent

https://greprepclub.com/forum/percentages-18135.html

Shouldnt the answer to this question be D? Since we can't tell the original price amount?
greenlight-admin's picture

No, the answer will always be B.
Here's my full solution: https://greprepclub.com/forum/john-buys-a-shirt-at-80-of-its-tagged-pric...

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