How much would $100 invested compounded continuously be worth after 15years round your answer to the nearest cent?

Total = Principal * e ^ (rate*years)
where "e" is the mathematical constant 2.718281828459
This can't be answered because you didn't state the rate.

If the rate is 1 per cent then:
Total = Principal * e ^ (.01*15)
Total = Principal * e ^ .15
Total = 100.00 * e ^ .15
Total = 100.00 * 1.1618342427
Total = 116.18

If the rate is 12 per cent then:
Total = Principal * e ^ (.12*15)
Total = 100 * e^1.8
Total = 100 * 6.0496474644
Total = 604.96

Source:
http://www.1728.org/rate2.htm