When interest is compounded continuously, the amount of money increases at a rate proportional to the amount S present at time t, that is, dS/dt = rS, where r is the annual rate of interest.

(a) Find the amount of money accrued at the end of 5 years when $5000 is deposited in a savings account drawing 5 3/4% annual interest compounded continuously.

(b) In how many years will the initial sum deposited have doubled?

(c) Use a calculator to compare the amount obtained in part (a) with the amount S = 5000{1 + ¼ (0.0575)}⁵⁽⁴⁾ that is accrued when interest is compounded quarterly.