Allan deposits $1,000 into a bank account that pays 3% interest annual

Question

Allan deposits $1,000 into a bank account that pays 3% interest annually. If he makes no other deposits or withdrawals, approximately how much money is in the account after four years?

A. $120
B. $126
C. $1,120
D. $1,126
E. $1,200

eswarchethu135 · Answer

Amount =  (1.03)^4 * $1000

approx Amount = $1,126

OPTION:  D

ritu1009 · Answer

How have you taken it as compounded annually?

adstudy · Answer

Here we are depositing $1000 in the first year and that is the only deposit we make. 
So after 1 year the amount in the bank becomes $ 1030 ($1000 + 3% of 1000)

Now as we are not depositing anything after the first year, then bank will consider $1030 as the amount in bank and calculate your 3% over that.

Same thing will happen for the next two years. And after 4 years we would have an approximate of $1126 in our account, which is what has been asked in the question.

Hope it clarifies things. Please let me know in case of any query.

ritu1009 · Answer

Thanks for giving such nice explanation but I am still confused why the answer is not C.
i.e1000+( 1000*3*4/100) = 1120

adstudy · Answer

Hi  ritu1009 ,

Here in your calculation I can see you are using the formula of Simple Interest. Now we use simple interest when we have to calculate interest on the same principal amount that was deposited initially, that is if after 10 years also we need to calculate interest, it will be on the same principal amount.

Now Compound interest is the interest calculated on the initial principal plus all of the accumulated interest of previous periods of a deposit.

Now banks do exactly this. Hence we are calculating compound interest and not simple interest.

Hope it helps.

KHow · Answer

Thank you eswarchethu135.

I am wondering, though, how to do this calculation without a calculator on the GMAT exam. Could you or someone please provide some clarity about how to solve this on the GMAT in the 2 min timeframe without a calculator? Is there a trick to it that I am missing?

Thank you!

KHow

varun325 · Answer

HERE CALCULATE YEARLY IT CAN BE SOLVED IN 2 MIN TIME
INTEREST FOR THE FIRST YEAR
1000*3/100=30 ( ADDING IN PRINCIPLE)
INTEREST IN 2ND YEAR
1030*3/100=30.90 ( SIMPLE CALCULATION)
( ADDING IN AMOUNT OF 1 ST YEAR)
1060.90*3/100=31.83 ( THIS IS TIME CONSUMING)
 ADDING IN AMOUNT OF 2ND YEAR
NOW PRINCIPLE FOR 4TH YEAR=1092.73
NOW PLZ NOTE YOU NEED NOT CAL THE INTEREST FOR THE LAST I.E FOURTH YR 
IF WE FOLLOW THE PATTERN ,THE INTEREST FOR THE 4TH YEAR WILL BE AROUND 33.00
ADDING IN THE AMOUNT OF 3RD YEAR THE AMOUNT AFTER FOURTH YEAR WILL BE AROUND 124-126

EgmatQuantExpert · Answer

Hey  KHow ,
You can use the A-B method to find the net interest rate.
This method you can use in Test conditions also.

Regards

EgmatQuantExpert · Answer

Solution

Given:  
 • Allan deposits $1,000 into a bank account.
• Interest rate is 3% annually.

To find:  
 • The amount in bank account after 4 years if no deposits or withdrawal is made in this period.

Approach and Working:  
 • 3% interest will be levied each year.
 o So, this is a case of successive interest.
o Hence, we can use the A-B formula.

Note: If A and B are successive interest rate, then net interest rate = A +B +  \frac{A × B}{100}

• At the end of 1st year, net interest rate = 3%
• At the end of 2nd year, net interest rate = 3 + 3 + \frac{9}{100}  = 6+0.09 = 6.09
• At the end of 3rd year, net interest rate = 3 + 6.09 + \frac{3 × 6.09}{100}  = 9.09 + 0.1827 = 9.2727
• At the end of 4th year, net interest rate = 3 + 9.2727 + \frac{3 × 9.2727}{100}  = 12.2727+0.28 = Approx 12.56

Therefore, net interest rate levied on 1000 is 12.56%.

• Thus, amount after 4 years = 1000 +12.56% of 1000 = 1000 + 125.6 = 1125.6

Hence, approximately $1126 is in the bank account after 4 years.

Therefore, the correct answer is option D.
 
  Answer: D

Asariol · Answer

Is the only indication that this is compound interest the fact that the "bank" is paying it? I see no other indicators that this is not simple interest.

rounakkedia172 · Answer

A quick solution to this would be find the simple interest, i.e., 30*4 = 120, total amount according to Si method = 1000+120 = 1120,
But since we have a compound interest here, note that the interest rate and years both are not too high to make a huge difference, so the actual amount would be slightly above 1120, only option D fits the bill.

Fdambro294 · Answer

This is not the best written question.

I don’t think the wording of the question would meet GMAT standards.

From the wording “3% interest annually” we are supposed to infer that the compounding period is yearly, rather than quarterly or semi-annually.

I can’t imagine any official question being this vague.

Posted from my mobile device

jamiedimonn · Answer

how do u calculate or guess 1.03 pow 4 without using calculator?  Bunuel

egmat · Answer

Hi jamiedimonn,

Good instinct to worry about this, because you're right that fully multiplying  1.03 × 1.03 × 1.03 × 1.03  by hand is slow and error-prone. The trick on the GMAT is that you almost never need the  exact  value - you estimate and then let the answer choices do the rest.

Step 1: Get a floor with simple interest

Start with the easy version - plain (simple) interest:

-  3%  per year ×  4  years =  12%  total
-  12%  of  $1,000  =  $120  interest - about  $1,120

That's the floor. It's what you'd get with  no  compounding.

Step 2: Compounding only adds a little on top

Compound interest means you also earn "interest on the interest." With a small rate ( 3% ) over just  4  years, that extra is tiny - a few dollars, not hundreds. So the true amount is  a little above $1,120 , and nowhere close to  $1,200 .

Look at the choices:  C  is  $1,120  (exactly the simple-interest floor) and  D  is  $1,126  (just above it). Since compounding pushes you a bit past the floor,  D  is the only one that fits. You never had to nail the exact power.

If you do want the actual number

Square in two easy steps instead of multiplying four times:

-  (1.03)2  =  1.0609 
-  (1.0609)2  ≈  1.126

So  1000 × 1.126 ≈ $1,126 . Same answer, much less arithmetic.

Lock the habit in

Try estimating  (1.02)3  the same way:

- Simple:  2%  ×  3  =  6%  - floor of about  1.06 
- Compounding nudges it just over - roughly  1.061

Same move every time:  find the simple-interest floor, add a small bump, then pick the choice just above it.

Answer: D

Allan deposits $1,000 into a bank account that pays 3% interest annual

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