Question

Consider a contract that pays out $1,143 in 6 months, $101 in 12 months, $62 in 18 months, $30 in 2 years. Price this contract, assuming the following yield curve:

time	spot rate
6-month	1%
12-month	2%
18-month	2.5%
24-month	2.8%

Assume semi-annual compounding. Round your answer to the nearest cent (2 decimal places).

Answer 1

Cashflow at 6 months = ,1,143

Spot rate at 6 months = 1%

PV of CF at 6 months using spot rate = (1143) / (1+1%/2)¹ = 1,137.31

Cashflow at 12 months = 101

Spot rate at 12 months = 2%

PV of CF at 12 months using spot rate = (101) / (1+2%/2)² = 99.01

Cashflow at 18 months = 62

Spot rate of 18 months = 2.5%

PV of CF at 18 months using spot rate = 62 / (1+ 2.5%/2)³ = 59.73

Cashflow at 2 years = 30

Spot rate at 2 years = 2.8%

PV of CF at 2 years using spot rate = 30 / (1 + 2.8%/2)⁴ = 28.38

Sum all the PV to find the Price of the contract

Price of the contract = 1,137.31 + 99.01 + 59.73 + 28.38 = 1,324.43