Question 178354
The first thing we need to know for this problem is the formula for continuous compounding.  With an initial amount (principal) of P, a rate r, and a time t, the amount is
{{{A=Pe^(rt)}}}
So for our first situation, P=500, r=0.02, and t=5.  So the amount in the account after 5 years would be
{{{A=500e^(0.02*5)=552.59}}}
So the amount of interest would be 552.59-500=$52.59.
For the second situation, P=500, r=0.045 and t=5.
{{{A=500e^(0.045*5)=626.16}}}
So the amount of interest would be 626.16-500=$126.16.