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# PRMIA Exam 8006 Topic 10 Question 56 Discussion

Actual exam question for PRMIA's Exam I: Finance Theory, Financial Instruments, Financial Markets ? 2015 Edition exam
Question #: 56
Topic #: 10
[All Exam I: Finance Theory, Financial Instruments, Financial Markets ? 2015 Edition Questions]

Calculate the settlement amount for a buyer of a 3 x 6 FRA with a notional of \$1m and contract rate of 5%. Assume settlement rate is 6%.

An m x n FRA is an agreement to borrow money for a period starting at time m and ending at time n at the contracted rate. Therefore, the buyer of the 3 x 6 FRA has committed to borrow \$1m at the beginning of 3 months and return it at the end of 6 months, ie a total borrowing period of 3 months at a rate of 5%. Of course, the \$1m is never actually exchanged, and at the beginning of the 3 month period when the next three months' interest rate is known (6%), the parties merely exchange the difference in the interest. SInce this interest was only due at the end of the 6 months and is being exchanged at the 3 month time point, it will have to be discounted to its present value.

The correct answer to this question is =(1,000,000 * (6% - 5%) * 3/12)/(1 + (6%*3/12))=\$2463.05. Since interest rates rose, the borrower gained as he has the right to borrow at a lower rate, and therefore the seller will pay the borrower.

(Here:

- \$1m is the notional

- 6% - 5% represents the difference between the contracted and the realized interest rates

- 3/12 is the 3 month period from month 3 to 6

- Finally, we divide by the current interest rate for 3 months to present value the payment from month 6 to month 3)