A bank will pay you 5% interest on a deposit for three years, but forgets to specify the daycount basis or compounding frequency of the rate. You find yourself in the fortunate position of being able to choose monthly, semi-annual or annual compounding; and 30/360, act/360 or act/365 daycount basis. Which daycount and frequency combination should you choose?

A simple interest rate of r for N years means a $100 investment becomes $100(1 + rN) at maturity N. (In other words, there is no compounding.)

(a) For simple interest rate 5% for 10 years, calculate the equivalent interest rate with (i) annual, (ii) quarterly and (iii) continuous compounding. Assume 30/360 daycount.

(b) Show that if simple interest of r for T years is equivalent to interest rate r' with annual compounding then r' towards 0 as T towards infinity.