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# Continuous Compounding, Forward Rate, Value of FRA

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These questions are adapted from Fundamentals of Futures and Options Markets, 7th ed., John C. Hull.

Chapter 4

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.

Q I: What are the rates with continuous compounding?

Q2: What is the forward rate for the six-month period beginning in 12 months (i.e., F12.1 8)?

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. See pages 90-93.

#### Solution Preview

Hi Dear,

Find attached solutions to your questions.

Regards.

Solutions:

Question 1
The equation required for solving question 1 is given as:

Rc = m*ln(1 + Rm/m)

where:
Rc = continuous compounding rate; Rm = equivalent rate with compounding m times per annum.
Note: You can see this equation in the following book "Options, Futures, and other Derivatives - 7th Edition by John C. Hull". It is given as equation 4.3 in the book.
For our question, m = 2 (semi-annual ...

#### Solution Summary

This solution helps answer questions regarding continuous compounding, forward rate and value of FRA.

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