Financial Derivatives and Risk Management

I.An interest rate is quoted as 6% per annum with semi-annual compounding.

(1) What is the equivalent annual compounding rate?

(2) What is the equivalent continuous compounding rate?

II. The zero rates are given in the following table. Please calculate the value of a 2-year bond with a face value of $100 and 8% annual coupon rate (coupons are paid semiannually).

Maturity (years)          Zero rate (continuous compounding)

0.5                               3%

1.0                               3.25%

1.5                               3.50%

2.0                               4.0%

III. The 3-month T-bill with a face value of $100 is selling for $98 today. T-bills don't pay any coupons. The only payment to investor is the face value at maturity. Given this information, what is the continuous compounding zero rate for three months?