Question 775679
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(1 + R*T)}}}
{{{100 = 500RT}}}
{{{RT = 1/5}}} ________ (i)


If the rate of interest is one fourth more than the existing rate then it becomes {{{R + R/4 = 5R/4}}}% 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(1 + (5*R/4)*2T)}}}
{{{A = 500(1 + (5/2)*RT)}}}
{{{A = 500(1 + (5/2)*(1/5))}}} [substituting value of {{{RT}}} from (i)]
{{{A = 500(1 + 1/2)=500*(3/2)=750}}}


Hence, the accumulated value would be 750 Euros