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Alex deposited x dollars into a new account that earned 8

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Re: Alex deposited x dollars into a new account that earned 8  [#permalink]

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New post 19 Sep 2019, 23:27
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shreyagupta1401 wrote:
yonseiglobalstudent wrote:
BrainLab wrote:
See attachment for the solution



I just want to clarify one point. I follow up until the start of the 2nd year, but then why do we multiply again by 1.08? (2.08x)(1.08)
Where did the 1.08 come from? I believe we need to represent 8% of 2.08x, but why don't we multiply by .08 instead?


I have the same question. Can someone please explain clearly why we are multiplying by 1.08 and not 0.08 at the end of the second year?


Interest earned at the end of the second year would be 2.08x*0.08 but the balance at the end of the second year would be (amount at the beginning of the second year) + (interest earned in second year) = 2.08x + 2.08x*0.08 = 2.08x*1.08.

Hope it's clear.
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Re: Alex deposited x dollars into a new account that earned 8  [#permalink]

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New post 11 May 2020, 16:06
yonseiglobalstudent wrote:
BrainLab wrote:
See attachment for the solution



I just want to clarify one point. I follow up until the start of the 2nd year, but then why do we multiply again by 1.08? (2.08x)(1.08)
Where did the 1.08 come from? I believe we need to represent 8% of 2.08x, but why don't we multiply by .08 instead?



Hi! I just figured this out so here’s my explanation:

To grow anything by a percent, you’re essentially adding 1 to that percent. So in this case growing by 8 percent is equivalent to 1.08

1st year : x + x(.08) = 1.08X
2nd year is (1.08x + x ) .08 while you can do this, it’ll multiple out to be this ugly ugly UGLY number. So to simplify your life, simply change .08 to 1.08 because growing 8 percent is the same as 1.08 growth.

Example: principle is $100 interest is 4% how much is the total at the end of 2 years.

1st year is 100 + 100(.04) = 104
2nd 104 + 104(.04) = 108.16 that’s the same method as the above example if you multiplied by .08 but because these are easy numbers you can figure it out quickly. However you can cut the steps shorter if you simply did

104 x 1.04 = 108.16 same answer, less ugly.

Also as I mentioned, I just put this logic together so if I’m wrong, I’m so sorry!

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Re: Alex deposited x dollars into a new account that earned 8   [#permalink] 11 May 2020, 16:06

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Alex deposited x dollars into a new account that earned 8

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