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

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

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New post 08 Nov 2018, 00:14
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A
B
C
D
E

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  45% (medium)

Question Stats:

65% (01:46) correct 35% (01:07) wrong based on 130 sessions

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Re: Allan deposits $1,000 into a bank account that pays 3% interest annual  [#permalink]

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New post 08 Nov 2018, 03:38
Amount = \((1.03)^4 * $1000\)

approx Amount = $1,126

OPTION: D
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Re: Allan deposits $1,000 into a bank account that pays 3% interest annual  [#permalink]

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New post 08 Nov 2018, 03:45
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eswarchethu135 wrote:
Amount = \((1.03)^4 * $1000\)

approx Amount = $1,126

OPTION: D



How have you taken it as compounded annually?
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Re: Allan deposits $1,000 into a bank account that pays 3% interest annual  [#permalink]

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New post 08 Nov 2018, 04:37
ritu1009 wrote:
eswarchethu135 wrote:
Amount = \((1.03)^4 * $1000\)

approx Amount = $1,126

OPTION: D



How have you taken it as compounded annually?


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.
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Re: Allan deposits $1,000 into a bank account that pays 3% interest annual  [#permalink]

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New post 09 Nov 2018, 00:45
adstudy wrote:
ritu1009 wrote:
eswarchethu135 wrote:
Amount = \((1.03)^4 * $1000\)

approx Amount = $1,126

OPTION: D



How have you taken it as compounded annually?


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.


Thanks for giving such nice explanation but I am still confused why the answer is not C.
i.e1000+( 1000*3*4/100) = 1120
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Allan deposits $1,000 into a bank account that pays 3% interest annual  [#permalink]

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New post 09 Nov 2018, 19:13
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ritu1009 wrote:

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


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.
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Re: Allan deposits $1,000 into a bank account that pays 3% interest annual  [#permalink]

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New post 06 Dec 2018, 09:27
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


eswarchethu135 wrote:
Amount = \((1.03)^4 * $1000\)

approx Amount = $1,126

OPTION: D
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Re: Allan deposits $1,000 into a bank account that pays 3% interest annual  [#permalink]

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New post 26 Jun 2019, 17:45
KHow wrote:
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


eswarchethu135 wrote:
Amount = \((1.03)^4 * $1000\)

approx Amount = $1,126

OPTION: D


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

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New post Updated on: 27 Jun 2019, 03:43

Originally posted by EgmatQuantExpert on 27 Jun 2019, 03:34.
Last edited by EgmatQuantExpert on 27 Jun 2019, 03:43, edited 1 time in total.
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Re: Allan deposits $1,000 into a bank account that pays 3% interest annual  [#permalink]

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New post 27 Jun 2019, 03:39
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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
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Re: Allan deposits $1,000 into a bank account that pays 3% interest annual   [#permalink] 27 Jun 2019, 03:39
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