3. An investment pays interest to the investor n times per year, at a notional annual rate of 3%. This means that, each time the account pays interest, the value of the investment increases by-%. n (a) Show that, each year, the investment actually grows by r%, the equivalent annual rate, where 71 3 1+ 100=(1 100m (b) Calculate the value of r when interest is paid quarterly, so n = 4. (c) Calculate the continuously compounded rate, which the limiting value of r as n in- creases towards infinity. Your answers to parts (b) and (c) should be expressed to at least three decimal places.