I am having some troubles understanding this topic of interest rates.
For example, if i invest 1 dollar at a continuous compounding rate of 11% , then my end of year value is equal to $e^{0.11}=1.116$ dollars. From here it says that investing at 11% a year continuously compounded is the same as investing 11.6 a year annually compounded.
Now where is this 11.6 coming from ? Is it coming from the 1.(116) dollars value? So i just take the decimal 0.116 and transform it into a percentage?
Another question I have regards this problem:
Suppose the annually compounded rate is 18.5%. The present value of a $100$ perpetuity, with each cash flow received at the end of the year, is $100/.185 =\$540.54.$ If the cash flow is received continuously, we must divide \$100 by 17%, because 17% continuously compounded is equivalent to 18.5% annually compounded (with the explanation that $e^{0.17}=1.185).$
What is the relationship between the annually compounded rate and the continuously compounded rate ? How do I use one to calculate the other ? I am very confused.