If the 3 month interest rate is 5%, and the 6 month interest rate is 6%, what would be the contract rate applicable to a 3 x 6 FRA?

If the 3 month interest rate is 5%, and the 6 month interest rate is 6%, what would be the contract rate applicable to a 3 x 6 FRA?
A . 6%
B . 6.9%
C . 5.5%
D . 5%

Answer: B

Explanation:

The correct answer is Choice ‘b’, as this question is merely asking for the forward rate based on known spot rates. The forward rate applicable to the three month period commencing in 3 months time is given by [(1 + 6%*6/12)/(1 + 5%*3/12) – 1]*4 = 6.91%. Thus Choice ‘b’ is the correct answer.

Here is a step by step way to think about it: $1 invested now at 6% for 6 months grows to (1 + 6%*6/12)=1.03. At the same time, using the 3 month rate, $1 invested now at 5% for 3 months grows to (1 + 5%*3/12)=1.0125. Effectively, this means that the 1.0125 at the end of 3 months grow to 1.03 at the end of 6 months, implying the rate of interest during the 3 months from 3 to 6 months is (1.03/1.0125 – 1)*4 = 6.91%.

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