The 6-month, 12-month, 18-month, and 24-month zero rates are 3.00%, 3.50%, 4.00%

Question

The 6-month, 12-month, 18-month, and 24-month zero rates are 3.00%, 3.50%, 4.00%, and
4.50% with semi-annual compounding.
Q1: What are the rates with continuous compounding?
Q2: What is the forward rate for the six-month period beginning in 12 months (i.e., F12,18)?
Q3: What is the value of an FRA that promises to pay you 5.50% (compounded semi-annually)
on a principal of $1 million for the six-month period starting in 12 months? Hints: you must
convert your continuous rate calculated in Q2 to semi-annual to determine the current forward
rate for the FRA; you must remember that the contract covers only 6 months (one-half year) of
interest.
Please show how you arrive at the answer. I want to know how to compute these. Thank you!

Explanation / Answer

1. 3.5% 2. 4.5% 3. 12*5.5%=66

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