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 3 by - %. n (a) Show that, each year, the investment actually grows by r%, the equivalent annual rate, where n r 3 1+ = + 100 100n (b) Calculate the value of r when interest is paid quarterly, so n = 4. (c) Calculate the continuously compounded rate, which is 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. 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 3 by - %. n (a) Show that, each year, the investment actually grows by r%, the equivalent annual rate, where n r 3 1+ = + 100 100n (b) Calculate the value of r when interest is paid quarterly, so n = 4. (c) Calculate the continuously compounded rate, which is 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