If the six-month interest rate is 6% and the one-year interest rate is 8%, what is the rate for an FRA over the period from six months to one year? Assume that the number of days up to six months is 182 and from six months to one year is 183
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To calculate the rate for an FRA (Forward Rate Agreement) over the period from six months to one year, we can use the formula:
FRA rate = (R2 - R1) x (T2 / (T2 - T1))
Where:
R1 = interest rate for the first period
R2 = interest rate for the second period
T1 = duration in days for the first period
T2 = duration in days for the second period
In this case:
R1 = 6%
R2 = 8%
T1 = 182 days
T2 = 182 + 183 = 365 days
Substituting these values into the formula, we have:
FRA rate = (8% - 6%) x (365 / (365 - 182))
= 2% x (365 / 183)
= 2% x 2
= 4%
Therefore, the rate for an FRA over the period from six months to one year is 4%.
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