If a $3,000 deposit is made into a savings account that pays 6 percent

Archit3110 You have an error in your equation. You have to divide r% by number of times the interested will be compounded, 12 in this case. Correct answer is C.

Amount = P(1+r%/n)^nt = $3,000(1+6/1200)^12 = $3000(1.005)^12 ~ $3,185

You could also have assumed taken this as a simple interest question to get $3,180. Answer will be a little bit more than this number since we are dealing with compound interest. So best answer is $3,185.

hi there funsogu have one question:

\(3000(1.062)^12\) how to calculate it without calculator (i mean when it is raised to 12th power) ;? any idea?

hi there funsogu have one question:

\(3000(1.062)^{12}\) how to calculate it without calculator (i mean when it is raised to 12th power) ;? any idea?[/quote]

Hi dave13. I am not an expert but sure I can help.

Firstly, what you are trying to determine is 3,000(1.005)^12 not 3,000(1.062)^12 . I was at a dilemma on how to solve this without calculator so I decided to just use simple interest and choose an answer that is slightly above the answer for simple interest ($3,180) and chose C since it is the closest. I then googled "how to solve compound interest rate questions fast" and came across this article (https://gmat.economist.com/gmat-advice/ ... ners-guide) by the theeconomist. Turned out they have the same approach. Hope it helps. Cheers!



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Solution:

We use the compound interest formula A = P(1 + r/n)^nt, where A is the ending amount, P is the starting amount (P = $3,000), r is the interest rate (r = 0.06), n is the number of times the interest is compounded per year (n = 12), and t is the number of years (t = 1).

The amount of money in the account, rounded to the nearest dollar, at the end of one year is:

A = 3000(1 + 0.06/12)^12 = 3000(1.005)^12 = $3,185

Answer: C

6% Compounded monthly for 1 year -----> 6% / 12 =

.05% Interest Compounded for each of the 12 months in the years (12 times)

Amount = $3,000 * (100% + .05%)^12


The Amount of Interest earned in month 1 = $3,000 * .05% = $3,000 * (1/200) = $15


In Month 2 , the Amount of Interest earned on the Interest from Month 1 will ONLY be ---> .05% * $15

From an approximation, we can see that the amount of Compound Interest earned on Interest will NOT be that much Greater than the Amount earned on Simple Interest


Thus, if we Calculate the amount that the Investment would have earned at SIMPLE INTEREST ---->

we can Estimate and say that the Amount earned at COMPOUND Interest will be SLIGHTLY MORE than the amount earned at Simple Interest


$3,000 * (.05%) = $15

At Simple Interest earned at the End of Each month for 12 months -----> $15 * (12) = $180 = Total Simple Interest earned

Amount that would have been earned at Simple Interest = $3,000 + $180 = $3,180

The Actual Answer should be SLIGHTLY LARGER > $3,180


-C- fits perfectly
$3, 185

Let us set up the equation required to calculate the amount.

When compounding is done monthly, Amount is calculated using the equation,

A = P \((1 + \frac{R }{ 1200}) ^ {12T}\),

Where P = Principal, R = Rate of Interest (in percent) and T = Period (in years)

In this question, P = 3000, R = 6 and T = 1

Substituting the values, we have, A = 3000 \(( 1 + \frac{6 }{ 1200} ) ^ {12}\)

Simplifying, we have, A = 3000 \(( 1 + \frac{1 }{ 200}) ^{12}\) or A = 3000 \(( 1.005) ^{12}\).

The obvious question that a lot of us will have on our minds will be, “How do I evaluate the exponent without a calculator?”. That is probably where GMAT does not expect you to be a number cruncher, but more of a smart estimator.

Now, 0.005 = ½ percent. ½ percent of 3000 would be 15; so, after 1 month, the amount would be 3015$.

Now, ½ percent of 15 = 0.0075, a very small value.

So, if we estimate that we would get a very small value above $15, for each of the 12 months, we wouldn’t be wrong at all.
Therefore, total interest in 12 months = 15 * 12 = 180.

So, is the amount 3180? NO. Remember that there is a small value over and above 15 in the interest component of every month after the 2nd month. Therefore, we need a value slightly above 3180, that would be 3185.

Answer option A is non-sensical. Answer options D and E are impossible to reach in one year considering the meager rate at which interest is being paid out.

The correct answer option is C.

We find out that the value of 3000(1.005)^12 is closest to either option B or C, but I eliminated option B and chose option C -> 3185 because the units digit (or atleast the last nonzero digit) in the value of 3000(1.005)^12 must be 5.