This client will buy a building a year from now to centralize its headquarters, currently scattered in five different locations. To do so, it will have to borrow 1.5M$. Given the inflationary environment, the client is afraid that interest rates will increase and would like to secure the interest rate on a 10-year loan today. The current interest rate today for 10 years is 2.50%. On the market, you find counterparties willing to enter an FRA at 2.75% for 10 years. What FRA (i.e. "FRA?x?") do you wish to build for this client? Will your client enter as the short or as the long? Then, after one year, the spot price for borrowing and lending for 10 years is 3.50%. Does your client gain or lose? What is the settlement amount on that date?

Professor said to use months for calculations.

I need an answer for the settlement amount with calculations and an explanation

My answer so far: enter 12x132 at 2.75% as long for an amount of $1,500,000 and I would be extremely grateful if you would tell me whether it's right or wrong and provide an explanation if it's wrong.