John deposited $10,000 to open a new savings account that

SOLUTION

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
(8) $10,101
(e) $10,200
(D) $10,201
(E) $10,400

Approach #1:
4 percent annual interest compounded quarterly --> 1% in 3 moths.

For the first 3 moths interest was 1% of $10,000, so $100;
For the next 3 moths interest was 1% of $10,000, plus 1% earned on previous interest of $100, so $100+$1=$101;

Total interest for 6 months was $100+$101=$201, hence balance after 6 months was $10,000+ $201=$10,201.

Answer: D.

Approach #2:
If the interest were compounded every 6 moths instead of every 3 months (quarterly) then in 6 months the interest would be 4%/2=2% of $10,000, so $200. Now, since the interest is compounded quarterly then there would be interest earned on interest (very small amount) thus the actual interest should be a little bit more than $200, only answer choice D fits.

Answer: D.

Hope it's clear.
_________________

john amount is compounded quarterly so the formula is A=P*(1+R/100)^N her p=principle R=rate of interest N=no of terms
rate of interest is 4% for a yr
so for quarter R=4/4=1%
john receive amt after 6 mnts so there are two quarter
so N=2
Amount A=P(1+R/100)^2
=10000(1+1/100)^2
=10000(1+0.01)^2
=10201

D.

SI = (P*R*T) / 100
SI after 1st Quarter: (10,000*4*3/12) /100 = 100
Principal for 2nd Quarter = 10,000+ 101 = 10100
SI after 2nd Quarter: (10,101*4*3/12) /100 = 101
Amount after 2nd Quarter (6 months) = 10100 +101 = 10,201

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_________________

10000*1,01*1,01 = 10201

I am new to the forum, starting on GMAT studying. I saw the solutions, but we are not using the calculator on test day so I do not understand thanks

Amount in John's A/c after 6 months = ($10,000 * 1%) + [($10,000 * 1%) * 1%] = $10,201. Ans (D).
_________________

Although this is the method they are looking for, the question is poorly worded. By explicitly saying that 4% was earned, this implies that 4% was the effective rate, and not nominal.
Would have been better to say "the account earned a nominal annual interest rate of 4%". No more confusion.

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
_________________

Since the interest is compounded quarterly it will increase by 1% every 3 months.

Start: 10,000

After 3 months(1 quarter): 10,000+10,000(.01)=10,100

After 6 months (2 quarters): 10,100+10,100(.01)=10,100+101=10,201

Hi All,

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:

GMAT assassins aren't born, they're made,
Rich

niks18 amanvermagmat Bunuel



For simplification of 10,000 * \((1.01)^2\) is my below approach valid:

10,000 * \((1.01)^2\)

= 101 * 101 or \((101)^2\) or\((100+1)^2\)

Now using \((a+b)^2\) we get \(100^2 + 2 * 100 * 1 + 1^2\) ie 10,201.
_________________

________________
Yes, that's correct.
_________________

Compounded quarterly means rate is divided by 4 and time is increased four times..
So RATE :- 4/4=1
TIME :- 6 months = 1/2 year = 4*1/2=2
So Amount after 6 months = \(10000(1+\frac{1}{100})^2=10000*(\frac{101}{100})^2=101^2=10201\)
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%
So, the interest for the next 3 months = 1% of $10,100 = $101
Total after 6 months = $10,100 + 101 = $10,201

Answer: D

Cheers,
Brent

WIth the logics in the replies after a year John will have app 10406,5, which is not 4% annual interest(((
I tried solving the problem with 10.000*n^4=10400, and 10.0000*n^2 being what we are looking for, and it equals to app 10.198
please help me understand why is my approach wrong

Hi LILICHKA,

When it comes to calculating interest, we have to pay careful attention to how the prompt tells us to calculate that interest. There are several factors to consider:

1) What is the interest rate and timeframe?
2) Are we calculating Simple Interest or Compound Interest (as those two options almost always lead to different results)?
3) If we are using Compound Interest, then how frequently is the interest compounded (since the greater the number of calculation 'periods', the greater the overall interest will be).

Here, we're given an interest rate of 4% annual interest and we're told that the interest is COMPOUNDED QUARTERLY. This means the interest is generated 4 times a year (re: every 3 months) - which also means that for each calculation, we use 4%/4 periods = 1% interest per period.

IF we were calculating interest for an ENTIRE YEAR, then using the Compound Interest Formula, we would have:

($10,000)(1.01)^4

However, we are asked for the interest after 6 months, which means that there are 2 periods...

($10,000)(1.01)^2

GMAT assassins aren't born, they're made,
Rich

Contact Rich at: Rich.C@empowergmat.com

but then it's more than 4% annually.
why don't we use 10.000*x^4=10.400, where x is the quarterly rate (and it's more than 1%?)