Question

Suppose the spot rates for 1 and 2 years are s1=6.3% and s2=6.9% with annual compounding. recall that in this course interest rates are always quoted on an annual basis unless otherwise specified. what is the forward rate, f1,2 assuming annual compounding?

Answer 1

To find the forward rate f1,2, we calculate the future values using the given spot rates and then solve for the forward rate. The calculation gives us a forward rate of 7.6418%, which equates the two-year investment return to the compounded one-year return.

Step-by-step explanation:

The question asks us to calculate the 1-year forward rate beginning 1 year from now, denoted as f1,2, given the 1-year and 2-year spot rates with annual compounding. In finance, this rate represents the future rate agreed upon today for a period starting in one year and extending for an additional year.

To compute the forward rate, we start by finding the future value of a one dollar investment for two years at the 2-year spot rate (s2) and then finding the future value of a one dollar investment for one year at the 1-year spot rate (s1). The forward rate is then the rate that equates these two future values at the end of the second year.

The formula to calculate the future value with compound interest is:

Future Value = Principal x (1 + interest rate)time

For the 2-year spot rate (s2=6.9%), the future value after 2 years would be:

1 x (1 + 0.069)² = 1 x 1.0692

For the 1-year spot rate (s1=6.3%), the future value after 1 year would be:

1 x (1 + 0.063)1 = 1 x 1.063

Now we set the future value using the 2-year spot rate equal to the future value using the 1-year rate compounded for another year at the forward rate (f1,2):

1 x 1.0692 = 1 x 1.063 x (1 + f1,2)

Solving for f1,2:

f1,2 = (1.0692 / 1.063) - 1

f1,2 = 0.076418 or 7.6418% when expressed as a percentage.

Therefore, the forward rate f1,2 is 7.6418%.

Answer 2

Since the problem assumes annual compounding, then the relationship of forward rate and spot rates is given in the equation:

f1,2 = ((s2^2 / s1) - 1)

Therefore,

f1,2 = ((1.069^2 / 1.063) - 1)

f1,2 = 0.075 = 7.5%

Forward rate is 7.5%.