Solve the Problem $\$ 1600$ Is Deposited in an Account with an Interest Rate Of Account

Multiple Choice

Solve the problem.
- $\$ 1600$ is deposited in an account with an interest rate of $\mathrm{r} \%$ per year, compounded monthly. At the end of 8 years, the balance in the account is given by $A=1600\left(1+\frac{r}{1200}\right) ^{96}$ . Find the rate of change of A with respect to $\mathrm{r}$ when $\mathrm{r}=10$ .

A) $\frac{\mathrm{dA}}{\mathrm{dr}}=283.93$
B) $\frac{\mathrm{dA}}{\mathrm{dr}}=129.07$
C) $\frac{\mathrm{dA}}{\mathrm{dr}}=130.14$
D) $\frac{\mathrm{dA}}{\mathrm{dr}}=281.58$