# Theoretical spot rates

Calculate the 1.5-year and 2-year theoretical spot rates if the 6-month spot rate is 1.75 percent and the 1-year spot rate is 1.95 percent. The 1.5-year note has a coupon of 3 percent and is selling for 101.3518. The 2-year note has a coupon of 4.5 percent and is selling for 104.5764. (Quotes are in decimals, not 32nds.)

Based on the data and the calculated answers above, calculate the six-month forward rate 1.5 years from now (1f3).

Please show all calculations.

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#### Solution Preview

The answers are in the attached excel file:

Calculate the 1.5-year and 2-year theoretical spot rates if the 6-month spot rate is 1.75 percent and the 1-year spot rate is 1.95 percent. The 1.5-year note has a coupon of 3 percent and is selling for 101.3518. The 2-year note has a coupon of 4.5 percent and is selling for 104.5764. (Quotes are in decimals, not 32nds.)

Based on the data and the calculated answers above, calculate the six-month forward rate 1.5 years from now (1f3).

Please show all calculations.

6-month spot rate= 1.75% or 0.0175

1-year spot rate= 1.95% or 0.0195

First we calculate 1.5 year and 2 year theoretical spot rates

The 1.5-year note has a coupon of 3 percent and is selling for 101.3518.

Coupon rate = 3% or 0.03

Assuming note makes semiannual coupon payments and using $100 as par value

Cash flow from the note:

There will be three cash flows; 6 month, 1 year and 1.5 year

0.5 year= $1.50 =0.5 x 0.03 x 100 (semi annual interest )

1 year= $1.50 =0.5 x 0.03 x 100 (semi annual interest )

1.5 year= $101.50 =0.5 x 0.03 x 100 + 100 (semi annual interest + principal)

P = ...

#### Solution Summary

The 1.5-year and 2-year theoretical spot rates have been calculated. Also, the six-month forward rate 1.5 years from now has been calculated.