$$$$2700\mathrm{.}002700\mathrm{.}00$

is deposited in an account with an interest rate of$$ r$\%$ per$$ year, compounded monthly. At the end of $8$ years, the balance in the account is given by

Upper A equals $2700\mathrm{.}00$ left parenthesis $1$ plus StartFraction r Over $1200$ EndFraction right parenthesis Superscript $96$ Baseline $.$A$=2700\mathrm{.}001+$r$120096.$

Find the rate of change of A with respect to r when r is

$10\mathrm{.}0010\mathrm{.}00\%.$

Question content area bottom

Part $1$

A$.$

StartFraction dA Over dr EndFraction equals $ $217\mathrm{.}80$dAdr$=$$$217\mathrm{.}80$

per$\%$

B$.$

StartFraction dA Over dr EndFraction equals $ $475\mathrm{.}17$dAdr$=$$$475\mathrm{.}17$

per$\%$

C$.$

StartFraction dA Over dr EndFraction equals $ $219\mathrm{.}62$dAdr$=$$$219\mathrm{.}62$

per$\%$

D$.$

StartFraction dA Over dr EndFraction equals $ $479\mathrm{.}13$dAdr$=$$$479\mathrm{.}13$

per$\%$