Question

Assuming the current zero rates (based on continuous compounding) for 6 months and nine months are 4% and 5% respectively. Assume further that a FRA was entered into several months ago that enables the holder to earn 6% (per annum based on quarterly compounding) for a 3-month period starting 6 months from now on a principal of $1,000,000. What is the value of the FRA to the person receiving funds?

Please show any formulas used.

Answer 1

Continuous Compounding Interest Formula = A = Pe^rt

^{Where, A = Maturity Amount / Final Amount, P = Principal, e = 2.7182, r = Interest Rate, T = Time in years}

Final Amount after 6 months = $1000000*2.7182^0.04*0.5

= $1020201.34

Final Amount after 9 months =$1000000*2.7182^0.05*0.75

= $1038212

Interest for 3 months period starting 6 months from now as per current rates = $1038212-1020201.34

= $18010.56........................(A)

Final amount as per FRA = P(1+r/n)^nt

Where, P = Principal, r = rate of interest, n = number of times per year interest is compounded, t = times in year

Thus, Final amount = $1000000(1+0.06/1)^1*0.25

= $1000000(1.06)^0.25

= $1014673.84

Interest for 3 months period starting 6 months from now as per FRA = $1014673.84 - 1000000

= $14673.84..............................(B)

Value of FRA = A - B

= $18010.56 - $14673.84

= $3336.72