This is from Hull, problem 6.16.
Suppose that it is February 20 and a treasurer realizes that on July 17 the company will have to issue \$5 million of commercial paper with a maturity of 180 days. If the paper were issued today, the company would realize \$4,820,000. (In other words, the company would receive \$4,820,000 for its paper and have to redeem it at $5,000,000 in 180 days' time.) The September Eurodollar future price is quoted as 92.00. How should the treasurer hedge the company's exposure?
So I know the relevant formula here for the number of contracts is $N=\frac{portfolioForwardValue}{futureContractPrice} \frac{portfolioDuration}{futuresDuration}$.
The given solution says $\frac{portfolioDuration}{futuresDuration} =2$ because the commercial paper's maturity is twice that of the future.
I don't understand this.
Isn't the treasurer's goal to ensure there will be \$5 million available in July? In that case $portfolioDuration$ is February to July while $futuresDuration$ is February to September. So shouldn't $\frac{portfolioDuration}{futuresDuration} = \frac{5}{7}$?