The MATH behind the interest rate.

For calculating option and future prices one uses so-called risk-free interest rates r, guaranteed interest you can collect without (reasonable) financial dangers involved. An annual interest of 6% means you start with e.g. $100 and after a year you have $100 + 6% of $100 = $106 . For the option prices you apply continuously compounded interest - you let the money work and collect interest on the interest, again interest on that interest and so on. The formula for that is

Money after one year = 
Money now times exp(annual rate in percent divided by 100)

exp is the exponential function you can find on any scientific calculator (or you can use our ON-LINE CALCULATOR). In the example we have

Money after one year = $100 * exp(0.06) = $106.18

The result is similar, somewhat higher because of the additional interest on the interest that was added up.

 

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