If the two year interest rate quoted today is 8.75% and the one year interest rate quoted today is 7.0%, what would be the one year forward rate?
10.53
To calculate the one year forward rate, we can use the formula:
(1 + f)^n = (1 + r2)^t / (1 + r1)^t
Where:
f = one year forward rate
n = number of years
r2 = two year interest rate
r1 = one year interest rate
t = length of time
In this case, we have:
(1 + f)^1 = (1 + 0.0875)^2 / (1 + 0.07)^2
Solving for f:
(1 + f) = ((1 + 0.0875)^2 / (1 + 0.07)^2)^(1/1)
(1 + f) = (1.1856 / 1.1449)^1
(1 + f) = 1.036264004
f = 1.036264004 - 1
f = 0.036264004
Therefore, the one year forward rate would be approximately 3.63%.
To find the one year forward rate, we can use the concept of forward rate agreements (FRAs). The FRA is an agreement between two parties to exchange a fixed interest rate on a notional amount for a specified future period.
In this case, we can assume that the forward rate is calculated based on the expectations of interest rates in the future. The difference between the two year interest rate and the one year interest rate gives us an indication of the market's expectations for the one year forward rate.
To calculate the one year forward rate, we can use the following formula:
Forward Rate = [(1 + Two Year Interest Rate) / (1 + One Year Interest Rate)] - 1
Plugging in the given values:
Forward Rate = [(1 + 0.0875) / (1 + 0.07)] - 1
Calculating the numerator:
(1 + 0.0875) = 1.0875
Calculating the denominator:
(1 + 0.07) = 1.07
Now, plugging in the calculated values:
Forward Rate = (1.0875 / 1.07) - 1
Calculating the division:
1.0875 / 1.07 = 1.0157
Finally, subtracting 1:
Forward Rate = 1.0157 - 1
Calculating the subtraction:
1.0157 - 1 = 0.0157
Therefore, the one year forward rate would be approximately 1.57%.