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OG John deposited $10,000

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OG John deposited $10,000

by AbeNeedsAnswers » Tue Jul 25, 2017 8:19 pm

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John deposited $10,000 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

D
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by Jay@ManhattanReview » Tue Jul 25, 2017 10:27 pm
AbeNeedsAnswers wrote:John deposited $10,000 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

D
We have,

1. Rate of interest = 4% per annum
2. Componung of interest = Quarterly; it means that after every quarter, the interest would be calculated. Since we have to calculate the sum at the end of the 6 months, the interest would be computed two times. Since the given rate = 4% is annual, we must get the quarterly rate, which is 4/4 = 1% per quarter

* Sum at the end of 3 months = 10,000 + 10,000*1% = 10,000 + 10,000*(1/100) = $10,100
* Sum at the end of 6 months = 10,100 + 10,100*1% = 10,100 + 10,100*(1/100) = [spoiler]$10,201[/spoiler]

The correct answer: D

Hope this helps!

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by Brent@GMATPrepNow » Wed Jul 26, 2017 6:27 am
AbeNeedsAnswers wrote:John deposited $10,000 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

D
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% of interest
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 [email protected] » Wed Jul 26, 2017 6:40 pm
Hi AbeNeedsAnswers,

We're told that a $10,000 investment earns 4% annual interest, compounded QUARTERLY (which means that we calculate interest 4 times per year). We're asked for the total value of the investment after 6 MONTHS. This question requires that you understand the concept behind the Compound Interest Formula (and this concept is sometimes referred to as "interest on top of interest").

If we were using SIMPLE Interest, then we'd calculate just once (and the total interest would be 4% of $10,000 = $400). However, when using Compound Interest, you calculate interest more than once per year, and you have to adjust the 'math' a bit. Based on the number of calculations that you do each year, you then have to divide the interest rate by that number of terms.

Here, we calculate 4 times per year, so each interest calculation is 4%/4 = 1%.

First 3 months = $10,000(1.01) = $10,100
Second 3 months = $10,100(1.01) = $10,201

Since the prompt asks for the total after 6 months, we don't have to do any additional work.

Final Answer: D

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by Scott@TargetTestPrep » Mon Aug 14, 2017 1:12 pm
AbeNeedsAnswers wrote:John deposited $10,000 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

D
Since the account compounds quarterly, John earns 0.4/4 = 0.1 or 1 percent interest each quarter.

After Q1, he earns 10,000 x 0.01 = 100 dollars interest, and thus he has a total of 10,000 + 100 = 10,100 dollars in the account after the first quarter or the first 3 months.

After Q2, John earns another 10,100 x 0.01 = 101 dollars interest.

So, after 6 months, the total amount of money in John's account is 10,100 + 101 = 10,201 dollars.

Alternate Solution:

We can use the compound interest formula A = P[(1 + (r/n)]^nt, with P = 10,000, r = 0.04, n = 4, and t = 0.5. Thus, we have P = 10,000[1+(0.04/4)]^2 = 10,000(1.01)^2 = 10,201.

Answer: D

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