Its in the FDP q bank

Question.
Donald plans to invest x dollars in a savings account that pays interest at an annual rate of 8% compounded quarterly. Approximately what amount is the minimum that Donald will need to invest to earn over $100 in interest within 6 months?

a) 1500
b) 1750
c) 2000
D) 2500
E) 3000

what i dnt understand is how can it be 100=.04 x.It will be compounded at the 3rd month
A= X + X x 8/100 x 3/12
then this amount A will be again invested and you will get an interest on that.so this is a two step process.
I tried back solving
2550x8/100x3/12 =50
amount is 2550
then 2550x8/100x2/12 =????
the only other thing I could think of was use simple interest and since that was 100 conclude that since in this prob it is CI it would be more and since only one compounding period has occurred this would be the minimum amount required, but this is a random thought process.

I also hv a general qs when u hv compound interest which is calculated quarterly and they say find the interest at the end of 6 months- why is the interest not just that of the first quarter-technically the second quarter is not over and therefore there is no interest-I dnt know know is I can explain in coherently!!Sorry
this thing has me confused :(

The interest after 6 months shall be:

x [1.02*1.02 -1]
= 0.0404 X
which is given as 100
so X is equal to 100/0.0404
~2500

The question only asks for a minimum amount and not the exact amount. So, we should choose from among the choices which satisfies the question.
if you calculate, Interest on 2500 is 101 which is what our question asks.

By the way, I guess you got 2550 as the answer since you had this confusion as to why we need to calculate the interest twice if the question says "end of 6 months"

Why do you say that end of 6 months is "technically not the end of 2nd quarter" ?

hi,
I was wondering if someone could explain this concept- I am confused!!!
Thanks
Ash

Hi Ash,
Atul has provided a nice explanation for how to do the problem. What specific part of the concept is confusing to you? If you can be more specific we can provide better help to you.

Thank you,

_________________
Jamie Nelson
ManhattanGMAT Instructor