Investor buys 90 day bank bill with face value $100 for $93.How do i calculate annual return & discount rate?

In addition to the above how do i calculate holding period yield on the above bill, if i purchase it at a market yield of 15% per annum, i hold it for 45 days & sell it at a yield of 14% per annum???
These questions hav been confusin me for sometime....can anyone help???

That first answer is a little off. The yields quoted are completely wrong for that dollar price for a 90 day bill.

also....if you buy something at 15% and later sell it for 14%...you actually have a taxable GAIN, not loss. And, the reason a bill changes price is because the market changes. There are no penalties for selling bills before they mature! There might be commissions if you are using a broker, but bill price changes are due to the bond market changing price.

A Treasury bill is by definition a Treasury debt instrument issued with 1 year or less to maturity. They are discounts, meaning the interest is the difference between the price you pay and the maturity value. If you hold a Tbill for 45 days, then your holding period is by definition 45 days.

In your case...buying a 90 day bill today at $93- is an annualized yield of 30.19% (US Treasury convention) or 30.438% (BEY).

If you bot it at 15%, then the price would actually be $96.395. If you waited 45 days and sold it at 15%, it would sell for 98.184...and that would NOT be a taxable gain. However, if you sold it for 14%, it would sell for 98.303 and you would have a taxable GAIN of the difference btwn 98.303 and 98.184.

There are various bond calculators available on the internet, dig around a bit.

Keep in mind the inverse relationship between price and yield and that should help alot.

This sounds like a zero coupon bond. To calculate the return, you would have to start on how much you've made relative to your investment in that time period. You make 100 in a year with an investment of 93. The difference is 7. What you need to do is divide the return (7) by your total investment (93) 7/93=.075269 Or an annual return of 7.5269%. Since your holding period is (90/360) .25 or the stated annual amount, then you multiply the annual return by .25 .75269% x .25 = 1.882%. Your return for the 90 day holding period is 1.882%. To calculate the $ return, you multiply your investment (93) by 1.882% or .01882 93x.01882 = 1.75. You'll get $1.75 in 90 days for your $93 investment.

If you buy an bill with a yield of 15% per year but sell it 45 days later at a yield of 14%, then either the bill is at a variable rate or you got penalized for taking your money out before the allotted time period.

The only way to calculate this would be by using a financial calculator or Microsoft Excel. What you are describing is similar to a T-Bill. To calculate the yield (T-Bill discount rate) you would use the TBILLYIELD function in Excel with the arguments of
=TBILLYIELD(settle,mat,pr).
Using this function would give you a yield of 30.1%.
To get the bond equivalent yield, you need to used the TBILLEQ function which gives you a yield of 33%.
To get an annualized return, you could use the RATE function which would give you a 34.22% return assuming 90 days out of a 365 day year.

um these last couple of answers don't know what their talking about. There is no way a bank bill will every be for 30% per annum in the US. They must have just punched it (incorrectly) into a financial calcualtor and didn't even think of how reasonable the answer sounds. The first guy is right