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by theachiever » Tue Dec 11, 2012 11:23 pm
John deposited 10000$ to open a new savings account that earned 4 percent annual interest,compounded quarterly.If there were no other transactions in the account,what was the amount of money in John's account 6 months after the account was opened?

A.10,100
B.10,101
C.10,200
D.10,201
E.10,400
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by Brent@GMATPrepNow » Tue Dec 11, 2012 11:29 pm
theachiever wrote:John deposited 10000$ to open a new savings account that earned 4 percent annual interest,compounded quarterly.If there were no other transactions in the account,what was the amount of money in John's account 6 months after the account was opened?

A.10,100
B.10,101
C.10,200
D.10,201
E.10,400
When the number of "compounding" periods is only 2 or 3, we can just calculate the interest for each period.
4% annual interest, compounded quarterly, means that for each quarter year (3 months), we are adding an interest of 1% to the amount in the bank. We can practically do this in our head.

Initial deposit = $10,000
Interest after 3 months = 1% of $10,000 = $100
Total after 3 months = $10,000 + $100 = $10,100

From here, the NEXT 3 months will yield an additional 1%
So, the interest for the next 3 months = 1% of $10,100 = $101
Total after 6 months = $10,100 + 101 = [spoiler]$10,201 = D[/spoiler]

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by puneetkhurana2000 » Wed Dec 12, 2012 12:03 am
We can use the formula as Amount after n quarters is P*(1+R/400)^n where P is the principal, R = Annual Rate of interest.

Plugging we get 10000*(1+4/400)^2 ... (6 months = two quarters)
=10201

Answer D
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