Marcus deposited $8,000 to open a new savings account that

8000 ( 1 + 5/200 )^(2*1)

Bumping for review and further discussion.

Yes: 5 percent annual interest compounded semi-annually --> 2.5% in 6 moths.

The basic formula for this question is compounded interest-

Payment(1 + r)^nt where

r= rate of interest- that is...how much percent?
n= number of times per year - this is key- this is what sets compounded interest apart from simple interest
t= year- or really this variable is just equal to 1- well for the sake of this formula on the GMAT- advanced finance is different

But the theory behind this formula is actually quite simple within the context of other GMAT percentage formulas...here's why. When we want to express a percentage increase such as a 20% increase of $100.00 on a stock then we would actually multiply the payment amount $100.00 by 1.2- if we wanted to express a 100% percent increase of that $100.00 we would multiply by "2" and if we wanted to express a 120 increase of $100.00 we would multiply by "2.2" - NOTE: a 150% increase is not the same as 150% of a number. The latter is warning is basically the idea of finance- you have a payment which is represented by P in the both the compounded and simple interested formula. The parentheses is quite simple if you understand the previously mentioned technique for percentage increase- the parentheses 1 + "r" or rate of interest is basically just that... we had 1 just like we did with a 20 percent increase of 1 ($100.00 x (1.2). The exponent in the formula simply expresses...well how many times are we doing that? So if you put down a $100.00 dollar stock on Tesla and it increases 20 percent every year then the amount we would have in two[u][/u] years is just $100(1.20)^2 which is really just $100(1 +20/100)^2 or in even in another form $100(1 +.20)^2

Anyways so what we have here is

$8,000.00(1 + .025)^2 ... this is the same as $8,000.00(1 + 25/100)^2 or even $8,000(1.025)^2

Thus
"D"

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