In: Finance
Year to maturity |
Par coupon yield to maturity (%) |
Calculated spot rates (%) |
Calculated forward rates (%) |
1 |
6.00 |
6.00 |
6.00 |
2 |
7.2 |
7.21 |
7.42 |
3 |
8.00 |
? |
? |
a) Using the data in the table above, calculate the three-year spot rate and the three years forward rate, assuming annual compounding. [4]
Assume, 1000 is the present value of future cash flows and annual cash flows are 70 each year.
Calculation of 3 years spot rate as follows,
1000 = 70/(1.06) + 70/(1.0721)^2 + 1070/(1+r)^3
1000 = 66.03773585 + 60.90142408 + 1070/(1+r)^3
873.06084007*(1+r)^3 = 1070
(1+r)^3 = 1.225573238
1+r = 1.0701
r = 7.01%------------spot rate
Calculation of 3 year forward rate as follows,
[(1+r)^3/(1.0721)^2] - 1 = [(1.0701)^3/(1.0721)^2] -1
= 1.0661 -1
= 6.61%-----------------forward rate