Consider annual compounding, monthly compounding, and the convergence to continuous compounding.
Continuous compounding involves the exponential function, which is its own first derivative. In terms familiar in this course, an account with continuous compounding increases at the rate R times the current balance.
The exponential function is interesting.
We learned to use Tables A, B, and C. Table C is the cumulative sums of Table A.
We put Tables A and C together to calculate the market values of a 30-year 10% coupon bond for various interest rates.