Grace makes an initial deposit of x dollars into a savings a

Hi Karishma,

taking B into consideration, we can have x=2, y=1, z=50.

so X after one year will be 3.

Y after one year and 4 interest bumps will be over 3....

Can you explain this?

How did you get that "Y after one year and 4 interest bumps will be over 3"?

If initial investment is $1 with an annual rate of 50% compounded quarterly, at the end of the year, the amount is 1(1 + 50/400)^4 = 1.608 i.e. somewhat above 1.5. How is it 3? Note that 50% is annual rate. If it is compounded quarterly, the quarterly rate becomes 50/4%

look at choice 2
grace=x(1+Z/10)
Georga= y( 1+z/100*4)^4

from 2 we have, y=zx/100, plug this into condition 2.

Geogra= zx/100(1+z/100*4)^4
it is clear that this expression is smaller than x(1+z/100) even if z=50

One doubt : If we are assuming that z=50, for Statement 2, why can't we assume the same for Statement 1 :

I mean, at the final stage we need to compare "x" with "y", since given that "x", "y" and "z" are positive numbers no greater than 50, why can't "x" = "y" = 50?

(Even though Statement 1 doesn't tell us about "x" or "y", we can assume right? Just as we assume for "z" in Statement 2)

If we substitute as above, we find "y" > "x".

So either Statement "1" or Statement "2" is sufficient right?

Kindly enlighten me.

What I did was:
A) clearly not sufficient because we don't know X and Y, what if X is 49 and Y is 1 or vice versa? Interest rates won't make a difference;

B) 100y=zx, y=zx/100, which means y principal amount equals to the interests of z;
and since z<50, then the interest of y, which is <y*50%, is definitely less than y,
therefore the interest of y is definitely is less than the interest of z

hello KarishmaB
Ma'am could you please explain how to decide after coming to this point
eq 1 : x(3/2)
eq 2 : x/2(9/8)^4
Going by the equation, using st-2, taking z = 50
I came up with this:

Grace's amount at the end of a year = x(1+ 50/100) ----- 1

and Georgia's amount at the end of a year = zx/100(1 + 50/400 )^4 ---- 2 "taking y=zx/100 from the st-2"

eq 1 : x(3/2)
eq 2 : x/2(9/8)^4

I could not just conclude equation is 1 > equation 2.... it took a lot of calculations like doing 9/8 and figuring out (9/8)^4

please help ESPECIALLY with how to come up with a conclusion in a situation such as this

Once you do some problems on compound interest, you realise that in the initial years, interest on interest is a small amount.

Also, half yearly compounding or quarterly compounding do give extra interest but slightly. The rate of interest is getting halved or quartered as the case may be in every half year or every quarter. After all, we are not using the rate of interest as 50% in each quarter. It becomes 50/4 = 12.5% in each quarter.
The power of compounding is seen over long term.

Try to keep a more big picture approach in mind instead of getting lost in algebra and equations. Once I realised that x will be at least twice of y from statement 2, and that the rate of interest will be maximum 50%, I know that 50% of x itself will give me the entire y amount. So 50% of y even if compounded quarterly cannot give me double of y. The quarterly compounding will make the interest on y more than y/2 but not by a whole lot.

Check out this video for compound interest in consecutive years: https://youtu.be/pfjZE2xcf04