Please help me solve this problem step by step. Thank you An investment of S10,000 earns interest at an annual rate of 7% compounded continuously. Complete parts (A) and (B) below.Click the icon to view the derivatives of exponential and logarithmic functions.(A) Find the instantaneous rate of change of the amount in the account after 1 year(s).$ 750.76 (Round to two decimal places as needed).(B) Find the instantaneous rate of change of the amount in the account at the time the amount is equal to $12,000.S 840.00° (Round to two decimal places as needed).

This question is based on the formula for compound interest and the derivative of the amount that is compounded continuously. Given : A0=principal =$10,000 Rate of interest=7% per annum. A. instantaneous rate of change of the amount after 1 year Formula for compounded continuously= A=A0e^rt for instantaneous rate of change we will find the derivative dA/dt=A0re^rt =10,000 x 0.07 x e^0.07 x1 =$750.76B. we have to find the time when A=12000 dollars using formula A=A0 e^r t 12000=10000 X e^ 0.07 X t 12000/10000=e^0.07t 1.2=e^0.07t Take natural log both sides ln 1.2=0.07 x t 0.182=0.07 x t t=0.182/0.07 t=2.60 put t=2.60 in the dA/dt equation calculated earlier dA/dt=A0re^rt =10000 x 0.07 x e^(0.07 x 2.60) =$840