Find the formula for A at any time t after the child is born.?

On the day a child was born, a lump sum P was deposited in a trust fund paying 5.5% interest compounded continuously. Use the balance A of the fund on the child's 25th birthday to find P. (Round to the nearest cent.)





A = $700,000





Find the formula for A at any time t after the child is born.





A = ?|||Recall that the formula for continuously compounded interest is:





A = P*e^(rt)





Since r = 0.055, A = 700,000, and t = 25, we obtain:





700,000 = P*e^[(0.055)(25)]


==%26gt; 700,000 = P*e^(1.375)


==%26gt; P ≈ $176,987.72





So P is about $176,987.72 and the formula for the amount at time T is:





A = (176,987.62)*e^(0.055t)





I hope this helps!|||the rate of change of the lumsum =





dA/dt= 1.055A





dt/dA= 1/ 1.055A





integrate





t= (1/1.055)lnA+C





at t= 0 A= P





0= (1/1.055)lnP + C





C= - (1/1.055)lnP





hence we get





t= (1/1.055)lnA - (1/1.055)lnP





rearrange for A





e^[1.055(t+(1/1.055)lnP)] = A