Differentiation: If you invest $X at an annual interest rate of r% compounded continuously. ?

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

No, the answer (b) is correct.

Differentiation of g(r) means the rate your money grows with respect to percent, not to time.  So increasing another percent would add approximately 165 at the end of the year.

Take care,

David

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