Effective Interest Rate - future Loan hedged with futures

Q. The CIO of a Canadian private equity company wants to lock in the interest on a three-month “bridge” loan his firm will take out in six months to complete an LBO deal. He sells the relevant interest rate futures contracts at 98.05. In six-months’ time, he initiates the loan at 2.70% and unwinds the hedge at 97.30. The effective interest rate on the loan is:

  1. 0.75%.
  2. 1.95%.
  3. 2.70%.

B is correct. The CIO sells the relevant interest rate future contracts at 98.05. After six months, the CIO initiates the bridge loan at a rate of 2.70%, but he unwinds the hedge at the lower futures price of 97.30, thus gaining 75 bps (= 98.05 − 97.30). The effective interest rate on the loan is 1.95% (= 2.70% − 0.75%).

This is one of those questions that is apparently easy but my brain makes it 10 times more complex and i cant figure out what i’m missing.

If someone takes out a $1,000 3mo loan at 2.70%, they pay (90/360)*2.70% * 1,000 = $6.75 in interest

If they sold $1,000 worth of 6mo futures, and price goes from 98.05 to 97.30, their profit is (.9805 -.9730) * 1,000 = $7.5

How can you combine those two things to get an effective payment of 1.95%?

I get that 2.7% minus 75bps is 1.95%, but how do you just completely ignore the concept of annualization for both the loan and the future contract, especially when one is 3mo term and the other is 6mo?

Appreciate any help un-engineering the way my brain works