What should the denominator be.

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What should the denominator be.

by gmatrant » Fri Aug 27, 2010 4:12 pm
At the same time that Rick opened an account
with $150 at Bank A, Mary Jane opened an
account at Bank B with $150. Mary Jane's
account has 10% simple annual interest and
Rick's gives 12% annual interest compounded
quarterly. If neither Rick nor Mary Jane make any
additional deposits or withdrawals, then what
percent more does Rick have in his account after
a year?

Ans is

[150 *(1.03)^4 - 150*(1.10)]
-------------------------------------
150*1.10


This is from Princeton. Just wanted to make sure the question is correct with respect to what it is asking for.
"what percent more does Rick have in his account after a year" -> Shouldn't the denominator be 150 and not 150*1.10.
Also in the numerator we should be subtracting 150.

Please explain.
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by Rahul@gurome » Fri Aug 27, 2010 5:58 pm
Solution:
When we have that the annual interest is 12% compounded quarterly, the interest rate gets one - fourth and the time is multiplied by 4.
So for Rick, amount is $150, time is 1 year and the annual rate of interest is 12%
Or at the end of 1 year, his amount becomes P[1 + r/(4*100)]^(4*1) = 150[1 + 12/(4*100)]^4 = 150[1 + 3/100]^4 = 150*[1.03]^4.
Mary Jane's account has 10% simple annual interest.
Or the interest for her at the end of 1 year is 150*10%*1.
So the amount for her at the end of 1 year is 150 + 150*10%*1 = 150*[1 + 10%] = 150*1.10.

The question is asking that what percent more does Rick have over Mary Jane's amount
Or the answer is [{150[1.03]^4 - 150*1.10}/(150*1.10)] * 100.
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by gmatrant » Fri Aug 27, 2010 9:00 pm
"what percent more does Rick have"
aren't you assessing Rick's initial amount Vs Rick's compounded amount- the percentage change here.
I am trying to understand where is the comparison with Jane's amount and Rick's amount being asked.

Please explain.

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by Rahul@gurome » Sat Aug 28, 2010 8:23 pm
Ideally the question should have stated clearly what exactly it is asking for,whether its Rick's amount over Mary Jane's amount or his own initial amount.
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