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Adam deposited a portion of his salary in a savings account in January

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Bunuel
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Adam deposited a portion of his salary in a savings account in January [#permalink] New post   20 May 2021, 03:45
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69% (01:51) correct 31% (01:46) wrong based on 68 sessions
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Adam deposited a portion of his salary in a savings account in January 2005. Adam earns a 10% interest compounded annually. If Adam plans to make a withdrawal of all the money in the account in January 2010, then his withdrawal is approximately what percent of his initial deposit?

A. 50%
B. 61%
C. 100%
D. 150%
E. 161%
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E
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Re: Adam deposited a portion of his salary in a savings account in January [#permalink] New post   20 May 2021, 05:22
Year: Percent of Original Investment Earned
1: 10%
2: 11%
3: 12.1%
4: 13.31%
5: 14.641%

Summing this gives ≈ 61%
This means that in 5 years he made around 61% off of interest. As he withdraws ALL of his money, the total withdrawal will be 100+61 = 161%

Answer E
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Re: Adam deposited a portion of his salary in a savings account in January [#permalink] New post   28 May 2021, 06:52
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Given
    • Adam deposited a portion of his salary in a savings account in January 2005
    • Interest earned = 10% CI annually.
    • Adam plans to make a withdrawal of all the money in the account in January 2010.

To find
    • The withdrawal amount will be what percentage of the deposit amount.

Approach and Working out:
After 2005, the deposited amount will earn interest for 5 years.
Let’s assume Adam deposited 100x.

By 2006 – 100x + 10x = 110x
By 2007 – 110x + 11x = 121x
By 2008 – 121x + 12.1x = 133.1x
By 2009 – 133.1x + 13.31x = 144.41x
By 2010 – 144.41x + 14.441x = 158.851x

Thus, his withdrawal amount will be approximately 161% of the deposit amount.

Hence, option E is the correct answer.
Correct Answer: Option E
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Re: Adam deposited a portion of his salary in a savings account in January [#permalink] New post   08 Jun 2021, 07:06
SI = P*R*T/100

SI = P*10*5/100 = 0.5P

Amount after 5 years = P+0.5P = 1.5P

Initial amount = P

1.5P/P*100 = 150%

Since, the Compound Amount will be more than 1.5P. Therefore, the percent value of the initial value will also be slightly more than this and the only option more than 150% is option E i.e 161%
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Re: Adam deposited a portion of his salary in a savings account in January [#permalink] New post   09 Aug 2021, 16:17
Must be over 100 eliminates ABC. Exponent of 5 indicates >1.5 giving E
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Re: Adam deposited a portion of his salary in a savings account in January [#permalink] New post   09 Aug 2021, 22:05
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Let Adam's salary was 100.

Interest rate: 10% (C.I.- annually)

Time: 5 years.

Amount after 5 years : \(100 ( 1+ \frac{10}{100})^5 = 100 * (\frac{11}{10})^5 = \frac{11^5 }{ 10^3}\)

Let the final amount is x% of the initial amount

=> \(\frac{11^5 }{ 10^3} = \frac{x}{100} * 100 \)

=> x = 161%

Answer E
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Re: Adam deposited a portion of his salary in a savings account in January [#permalink]
09 Aug 2021, 22:05
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