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Simple question on Interest / Principal

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Simple question on Interest / Principal

by amit1sharma » Tue Aug 31, 2010 4:48 am
An investment of 1 year certificate of deposit with annual rate of interest = 8% earned $ 1200 in one year. What fractional part of the interest would have to be re invested along the principal at the same rate in order to earn $ 1280 diring the second year.

Please explain step by step, especially the fractional part explanation.
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by kmittal82 » Tue Aug 31, 2010 5:06 am
Interest earned in 1st year = 8%

Let principle amount invested = x

0.08x = 1200 => x = 15,000

Let y be invested to earn 1280 at 8%

0.08y = 1280 => y = 16000

thus, we need to add $1000 to the principal to earn an interest of 1280

Initial interest earned = 1200, out of which we need to reinvest 1000 i.e. 1000/1200 = 5/6

whats the OA?
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by amit1sharma » Tue Aug 31, 2010 9:06 am
5/6 is the correct answer. Thank you so much.
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by Stuart@KaplanGMAT » Tue Aug 31, 2010 2:53 pm
amit1sharma wrote:An investment of 1 year certificate of deposit with annual rate of interest = 8% earned $ 1200 in one year. What fractional part of the interest would have to be re invested along the principal at the same rate in order to earn $ 1280 diring the second year.

Please explain step by step, especially the fractional part explanation.
A similar approach with less math:

We want to earn an extra $80 of interest. To earn $80 of interest at 8%, we must invest $1000.

(You can either figure that out intuitively or solve:

80 = (8/100)x
(100/8)*80 = x
1000 = x.)

So, we need to invest an additional $1000 out of the $1200 we earned last year:

1000/1200 = 10/12 = 5/6
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