The price of a 90-day Treasury bill is quoted as 10.00 . What continuously compounded return (on

step 1 Now here on this problem we are given that $1 ,000 is deposited in the saving account every year

The price of a 90-day Treasury bill is quoted as 10.00 ....

Key Concepts

Day Count Conventions (Actual/365 Basis)

Day count conventions are used to express the fraction of a year between two dates in financial calculations. The actual/365 basis is a convention that uses the actual number of days in the period divided by 365. This method is important for accurately converting returns on instruments with short maturities, such as Treasury bills, into annualized figures or into measures like the continuously compounded return.

Discount Yield and Quoted Price

In the context of Treasury bills, the quoted price often represents an annualized discount rate based on the face value of the bill, rather than a direct yield from price appreciation. This discount yield reflects the percentage by which the bill’s purchase price is lower than its redemption value, annualized according to a specific day-count convention.

Continuously Compounded Return

The continuously compounded return is a measure of return that assumes the reinvestment of earnings at every moment in time. It is calculated using the natural logarithm of the ratio of the final amount to the initial investment, and it is often used in financial models due to the mathematical convenience it offers, especially when dealing with differential equations and continuous time models.

Treasury Bills

Treasury bills are short-term debt instruments issued by the government that are sold at a discount to their face value. They do not pay periodic interest but instead provide a return by maturing at par value, with the difference between the purchase price and the redemption value representing the investor’s earnings.

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