The value of an investment increases by p% each month. If the investme

Question

The value of an investment increases by p% each month. If the investment was worth x dollars initially and y dollars after one month, then in terms of x and y, how much was it worth after two months?

A. y^2−x

B. x^2−y
 
C. xy/100
 
D. x^2/y
 
E. y^2/x

sashiim20 · Answer

Initial worth = $x
Value is y dollars after one month
Investment increases by p% each month.

y = p% of x =  \frac{xp}{100} 
p =  \frac{100y}{x}

Value after two months = p% of y 
 \frac{p}{100} * y  => (Can also write as  p * \frac{y}{100} )

Substituting value of p in above equation. we get;

\frac{100y}{x} * \frac{y}{100} = \frac{y^2}{x}.   Answer E...

amanvermagmat · Answer

Let x=100 and p=20. So after one month value of investment = 120, which is y. So y=120.

But next month again there is an increase of 20% over 120. So final value = 120% of 120 = 144.

So we are looking for an option where if we put x=100 and y=120, we should get '144'.

That is only option E.

y^2/x = (120^2)/100 = 144. Hence  E answer

ScottTargetTestPrep · Answer

We can create the following equation:
 
y = x(1 + p/100)
 
The above is the equation for the price at the end of the first month. So, after two months, the price should be x(1 + p/100)(1 + p/100) or x(1 + p/100)^2. 
 
Since y = x(1 + p/100), we see that 1 + p/100 = y/x. Thus, the price after two months is x(1 + p/100)^2 = x(y/x)^2 = x(y^2/x^2) = y^2/x. 
 
Answer: E

santosh93 · Answer

y = Intial value + Interest earned
 = x + p% of x
 =x +  \frac{xp}{100} 
 =x(1 +  \frac{p}{100} )

tanvi0915 · Answer

From the question we get
For first month:
y = x + x*p/100
y = x (1 + p/100)
Therefore p/100 = y/x - 1
For second month
= y + y * p/100
Substituting above eqn
= y + y(y/x -1)
= y + y^2/x -y
= y^2/x

chloreton · Answer

Assume easy values 
Let p=100% and initial amount =100
After 1 month, the value = 100*2 =200 =y
After 2 months, the value = 200*2=400

Here we need to put the value of x & y in option to get 400. Only  E  works.

Remember when the increase is 100 percent you multiply by 2; when increase is 200 percent you multiply by 3 and this goes on.

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