Question 693853
You probably misread the problem. What the problem asks is how much Charlie would have earned if He had invested in a different way. Charlie chose to invest a certain (unknown to us) sum of money he originally had for 5 years at a 7% interest rate. He earned $4,900 from that. What the problem asks is how much Charlie would have earned if he instead had invested that same unknown sum of money for 6 years at a 6% interest rate.
 
You could find the sum of money Charlie had originally invested to get the $4,900 in interest. 
Then, you could figure out how much interest he could get from that if he had invested it differently.
${{{x}}} = amount Charlie had invested originally
${{{5*0.07*x}}} = interets earned by investing ${{{x}}} for 5 years at 7%
We know that {{{5*0.07*x=4900}}}
{{{5*0.07*x=4900}}} --> {{{0.35x=4900}}} --> {{{0.35x/0.35=4900/0.35}}} --> {{{x=14000}}}
Investing that amount at 6% for 6 years, Charlie would have earned
{{{6*0.06*14000=highlight(5040)}}}
 
YOUR MISTAKE:
By multiplying the 6% rate times the 6 years times $4,900,
you were multiplying the 6% rate times the 6 years times the $4,900 interest Charlie had already earned. That would give you what Charlie could earn in the next 6 years by investing just the $4,900 interest he had already earned at a 6% interest rate. You added that to the $4,900 Charlie had already earned to find what Charlie could get in 13 years if he reinvests only the interest after the first 5 years.
 
FUN:
Unfortunately for Charlie, interests rates are very low nowadays.
However, if Charlie could reinvest his original $14,000 plus the $4,900 interest for one more year at 0.75% he could make another $141.75, which added to the prior $4,900 earning would bring his total earnings up to $5041.75 earned over the course 6 years.