Q1. The 6-month, 12-month, 18-month, and 24-month interest rates are 1.50%, 1.75%, 2.00%, and 2.25% with continuous compounding.
a. Calculate the present value of $100 in 1.5 years (=18 months).
b. Calculate are the equivalent 6-month, 12-month, 18-month, 24-month interest rates with quarterly compounding.
c. Calculate the 6-month forward rate between 1.5 years (=18 months) and 2 years (=24 months). Answer the forward rate with continuous compounding.
Q2. A short 18-month forward contract on a non-dividend-paying stock was entered into a year ago. The delivery price of the contract is $48.
Today, this contract has 6 months to maturity. The risk-free rate with continuous compounding is 2% per annum, the current stock price is $51. Calculate the value of this short forward contract.
Hint: value of short forward contract = value of long forward contract * -1