MathProblem 31 Compound interest problem #1

What is the value of $1, invested for one year at 100% interest, compounded infinitely?

Solution

Generally, the value of $1 invested for \(n\) years at interest rate \(i\), compounded \(x\) times per year:

\[(1+i/x)^{nx} \]

对于原问题，\(n=1,x\rightarrow \infin\):

\[\lim_{x\rightarrow \infin}(1+1/x)^x=e \]