Copy of Suppose you want to detemine the forward rates for your client, a lender who is considering a Forward Rate Ageement ( FRA). You have collected and organized the data for the risk-free zero interest rates with continuous compounding in the following table: Maturity( years) Zero Rate (% per annum) 1 2 2 3 3 5 4 6 5 7 What is the forward rate for the fourth year? (sample answer: 2.50%) Blank 1 What is the forward rate for the fifth year? (sample answer: 2.50%)
To determine the forward rates for a client considering a Forward Rate Agreement (FRA), we first need to understand what forward rates are and how they can be calculated from the given data. Forward rates represent the interest rates at which two parties agree to lend or borrow funds at a future date. In this context, we have collected data on risk-free zero interest rates with continuous compounding, and we want to find the forward rates for the fourth and fifth years.
The data we have gathered is as follows:
Maturity (years) | Zero Rate (% per annum)
-------------------------------------------
1 | 2
2 | 3
3 | 5
4 | 6
5 | 7
The forward rate for the fourth year can be calculated using the following formula:
���(4,5)=�5−�41+�4
Where:
Now, let’s calculate the forward rate for the fourth year:
���(4,5)=7%−6%1+0.06=1%1.06≈0.9434% per annum
So, the forward rate for the fourth year is approximately 0.9434%.
Moving on to calculating the forward rate for the fifth year, we can use the following formula:
���(5,6)=�6−�51+�5
Where:
Unfortunately, we don’t have the zero rate for year 6 in our data, so we can’t directly calculate the forward rate for the fifth year without that information. To determine the forward rate for the fifth year, we would need to obtain the zero rate for year 6 or additional data to estimate it.
In conclusion, we have calculated the forward rate for the fourth year, which is approximately 0.9434% per annum, based on the provided zero rates. However, we cannot calculate the forward rate for the fifth year without the zero rate for year 6. Forward rates are essential tools in finance for hedging interest rate risk and making informed lending or borrowing decisions.
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