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simple interest or compound interest for swap?

A $10 million 1-year semi-annual-pay LIBOR-based interest-rate swap was initiated 90 days ago when LIBOR was 4.8%. The fixed rate on the swap is 5%, current 90-day LIBOR is 5% and 270-day LIBOR is 5.4%.

To calculate the value to fix-paying-investor we need the discount rate.

in the answer, it calculate discount rate like: (1 + 0.05 × (90/360))

why not (1+0.05)^(90/360)?

why use simple interest rates?

Is that assumed that for all swap related calculation is based on simple interest calculation?

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On what occasion do we use Simple Interest rates?

Is there a standard of some sort?

The annualized rate is 5% not 105%

It sounds like ou’re just taking the 90 day libor and de-annualizing it and it happens to be used in the discounting.

Yes I am de-annualizing it on a compounded base.

The answer given is using Simple de-annualization. 90day’s interest is 90/360 of annual interest.

My question is, since a lot of fixed income calculation assume compounded interest rate, why do we use simple interest rate all of a sudden?

or it that I am just haven’t done enough question yet?

Swaps, Swaptions, & FRAs use this convention. The reason for it is that the LIBOR term structure is quoted in annualized terms. For example:

180-Day Rate: 6.0% (Actual 180 day rate = 6.0%*(180/360) = 3.0%
360- Day Rate: 7.0% (Actual 360 day rate = 7.0%*(360/360) = 7.0%

You just have to undo the convention for annualizing the rates.