Homework 3Q1. The 6 month, 12 month, 18 month, and 24 month interest rates are 2.00%, 2.25%, 2.50%,and 2.75% with continuous compounding.a. Calculate the present value of $100 in 2 years.b. Calculate are the equivalent 6 month, 12 month, 18 month, 24 month interest rates with semiannual compounding.c. Calculate the forward rate for the six month period beginning in 18 months. In other words,calculate the forward rate between 18 months and 24 months (i.e., F1.5,2). Answer the forward rate with continuous compounding.Q2. A short forward contract on a non dividend paying stock was entered into some time ago.Currently, it has 6 months to maturity. The risk free rate with continuous compounding is 3% per annum, the current stock price is $30 and the delivery price of the contract is $28. Calculate the value of this short forward contract.Q3. Suppose a bank needs to borrow (not lend) $50 million for 3 months starting in March 2017.Unfortunately, nobody knows what the 3 m borrowing rate will be in the future so the bank wants to hedge this interest rate risk.a. Devise a plan to lock in the borrowing rate today. Be specific about which futures contract how many contracts futures expiration month whether to take a long or short position of the contractb. Whats the 3m interest rate that the bank can lock in today? Use www.cmegroup.com to answer the actual interest rate in percentage per annum. Include the screenshot of the source.c. Suppose you are a speculator (not the bank above) and you think the interest rate will be higher than what you answered inb. What action should you take now in the futures market?Q4. Suppose a bank has unmatched asset and liability. Specifically, the bank has fixed rate loans as assets (receiving fixed rate interests) but has floating rate deposits as liability (paying variable rate interests). This is a risk to the bank because it can suffer a loss, if the floating rate increases over time. What can the bank do with swaps to eliminate this risk?
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