# Interest Rate Options: EAR

So, two types of EAR questions:

1. Borrow money and buy an interest rate call to cap borrowing costs

2. Lend money and buy an interest rate put to put a floor on lending rate recieved

Why, when calculating EAR, do you subtract the FV of the call from the net amount borrowed in the first example and add the FV of the put ot the amount lent in the second example.

Maybe I’m just tired, but can’t seem to get this logically…

when you borrow say 5 Million and also buy a Call Option .... you (the borrower) are receiving 5 Mill and paying the Call premium. So in terms of net inflows it is Amount Borrowed - Premium Paid. The Call option ensures that he does not pay more than a given interest rate each period. Similarly the Call Option payoff is REMOVED.

When a Lender offering 5 Million buys a Put Option - he has an outflow - both for the 5 Mill lent and the Put premium he pays to protect that he gets a minimum interest rate each period. Put Option Payoff is added.

There is also a collar, sell call buy put. I believe it was in last years PM mock. If you can do a collar problem, you can do both put and call … i would start there.

Right, but the collar question does not make you calc the EAR. EAR is only in the put / call LOS and the calculation has a few quirks.

I remember having to calculate EAR on the problem im referring to. Ill dig it up later… fairly sure it was the 2010 mock though.