There are two finance questions below:

Consider two of the conventions for quoting US interest rates:

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

(ii) annual compounding with act/360 daycount (conventionally denoted for y_AM 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.

A stock S with price at time t pays no dividends. If you own shares of S suppose that you can make some extra money by lending them to someone with the agreement that when they return the shares to you they will pay you b% of the final price as a fee for the loan. What is the formula for the value at time t of a forward contract to deliver the stock at time T for a price of K dollars? Assume the riskless interest rate at which you can borrow or lend money is r% for that exact period from t to T.