Chapter 11.7, Problem 65E

Work these exercises. (see Example 11.)

Finance An amount of $12,000 is deposited in an account with an interest rate of r percent per year, compounded monthly. At the end of 8 years, the balance in the account is given by

$A=12,000{\left(1+\frac{r}{1200}\right)}^{96}$.

a. Find $\frac{dA}{dr}$, the rate of change of A with respect to r.

b. Find $\frac{dA}{dr}$ when $r=4$ and interpret your answer.