One percent daily compounding over fifteen days

You put $100 into an investment that grows by $1\%$ each day, compounded daily. Rounded to the nearest dollar, what is it worth after $15$ days?

$116. The value is $100(1.01)^{15}\approx 116.10$. Mentally: simple interest gives $115, and compounding adds roughly $\binom{15}{2}(0.01)^2\cdot 100\approx 1.05$ more, so the total rounds to $116.