If you invest $X at an annual interest rate of r% compounded continuously. At the end of Y years. you have a ?

Question

If you invest $X at an annual interest rate of r% compounded continuously. At the end of Y years. you have a balance of B dollars where B = g(r). What is the financial interpretation of g'(5) = 165?

a. The balance grows at a rate of $165 per % when r = 5%

b. If the interest rate increases from 5% to 6%, you would expect $165 more in your account.

Are both of these correct??

Answer 1

Wikipedia is your friend:

http://en.wikipedia.org/wiki/Compound_in...

With provisos, "a" sounds right, but "b" is clearly false. The derivative is the slope at a point and a good linear approximation only in a "neighborhood" of the point. For exponential functions, a change of 20% and you are far from the neighborhood.