SOLUTION: At a certain rate of simple interest, 500 Euros will accumulate to 600 Euros after a certain period of time. Find the accumulated value of Euros at a rate of simple interest one f

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Question 775679: At a certain rate of simple interest, 500 Euros will accumulate to 600 Euros after a certain period of time. Find the accumulated value of Euros at a rate of simple interest one fourth as great over twice as long a period of time.

Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
Let the rate of interest be R % per year and time period be T years.
Therefore, the first scenario can be represented by the equation
600+=+500%281+%2B+R%2AT%29
100+=+500RT
RT+=+1%2F5 ________ (i)

If the rate of interest is one fourth more than the existing rate then it becomes R+%2B+R%2F4+=+5R%2F4% and double the previous time period is 2T years.

With this new set of rate of interest and time period, the accumulated value A would be:
A+=+500%281+%2B+%285%2AR%2F4%29%2A2T%29
A+=+500%281+%2B+%285%2F2%29%2ART%29
A+=+500%281+%2B+%285%2F2%29%2A%281%2F5%29%29 [substituting value of RT from (i)]
A+=+500%281+%2B+1%2F2%29=500%2A%283%2F2%29=750

Hence, the accumulated value would be 750 Euros