One percent daily growth for one hundred days

You put $100 into an investment that grows by $1\%$ every day, compounding daily. How much is it worth after $100$ days, to the nearest dollar?

$270. The value is $100\cdot1.01^{100}$. Since $100\ln1.01=100(0.01-0.00005+\dots)\approx0.995$, this is about $100e^{0.995}\approx270.48$, just under $100e$.