goodyear2013 wrote:
Julie put half of her savings in a savings account that pays an annual simple interest and half in a savings account that pays an annual compound interest. After two years she earned $120 and $126 from the simple interest account and the compound interest account respectively. If the interest rates for both accounts were the same, what was the amount of Julie's initial savings?
A) 600
B) 720
C) 1080
D) 1200
E) 1440
We need to find the amount off Julie's Initial savings...Let that be 2x
So x goes in simple interest and x goes in compund interest for a period of 2 years...
In case of Simple interest, The interest paid out is same for each year..Hence if $120 was interest for 2 years that means interest per year will be 60 $
So we have S.I,120 = \(\frac{x*2*R}{100}\)
or 6000 =x*R
For CI, in 126 $, 6$ represents nothing but interest earned on interest of 1st year.
In the First year, Interest amount is same for S.I and C.I
So we have
\(x(1+\frac{R}{100})^2-x= 126\)
or x(1 + R^2/10000+ 2R/100)-x=126
x+xR^2/10000+2xR/100)-x=126
x+R*6000/10000+12000/100-x=126
0.6R+120=126
0.6R=6 or R=10
So x=600...2x=1200 is the Initial savings.
_________________
“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”