# FRNs ```FRNs
FRNs = Floating Rate Notes
First issued in January 2014. New issues quarterly.
2-year notes
Interest payments are made quarterly, not semiannually
Interest (coupon) rates are the discount rates determined in the most recent auction of the
13-week (3-month) Treasury Bills, plus a spread (i.e.: 0.045%).
The spread is fixed for the life of the FRN and is determined during the FRN auction.
Investors bid for a spread at the auction just like they bid for a yield in other treasury
auctions.
Since 13-week T-bills are auctioned every week, the interest rate on an FRN changes
each week. However, interest accrues daily.
Unlike TIPS, the face value of FRNs doesn’t change – the interest rate changes.
Example:
You purchase a \$1,000 FRN at auction with a spread of 0.05% (five basis points).
There are 13 auctions of the 3-month T-bill between the date you purchase your FRN and
the first interest payment.
The discount rates (stop-out yields) for those 13 auctions are: 0.01%, 0.02%, 0.01%,
0.03%, 0.04%, 0.03%, 0.02%, 0.04%, 0.05%, 0.04%, 0.05%, 0.06%, and 0.07%.
Your first interest payment will be based on interest rates of: 0.06%, 0.07%, 0.06%,
0.08%, 0.09%, 0.08%, 0.07%, 0.09%, 0.10%, 0.09%, 0.10%, 0.06%, and 0.12%.
Since interest accrues daily, the daily rates (each week) are each of the above numbers
divided by 365. Each day, you earn that interest rate on a principal of \$1,000. So you will
earn 91 days of interest payments when you are paid your interest at the end of the
quarter.
To calculate this, take each of the above 13 rates and divide each by 365. Then add one to
each value. Since you get the same rate for 7 days in a row, raise each number to the 7th
power. Now multiply each of those 13 values together (this would be the same as
multiplying each of the 91 values together if the rate changed daily). Subtract one from
this product and multiply that by your \$1,000 principal. This should give you the amount
of interest you are paid at the end of the quarter. In this example, you would receive
\$0.2148173 – which would be rounded to 21 cents.
```