There are two financial problems related to interest rates:

(1) 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?

(2) Consider two of the conventions for quoting US interest rates:

(i) semi-annual compounding with 30/360 daycount (conventionally denoted y_SB for semi-bond since its used in the bond markets);

and (ii) annual compounding with act/360 daycount (conventionally denoted y_AM for annual-money, since its used in the money markets).

Derive an expression for y_AM in terms of y_SB. Remember that yields and interest rates are merely conventions for quoting how much money is to be paid or received. For simplicity, assume all years have 365 days.