Question

You bought a 1-year Treasury bill with a face value of $1,000 for $816.86. 9 months later, you sold it for $950.69.

What was your annualized return?

Can I see the formula to account for this answer?

Answer 1

Solution:

The formula for calculating the annualized rate of return is

= [ ( Sale Price / Purchase price ) ^1/n ] - 1

N = No. of years for which the investment was held

As per the Information given in the question we have

Sale Price = $ 950.69 ; Purchase Price = $ 816.86 ; N = ( 9 / 12 ) = 0.75 Years

Applying the above values in the formula we have

= [ ( $ 950.69 / $ 816.86 ) ^{( 1/0.75 )} ] - 1

= [ ( 133.83 ) ^{( 1.3333 )} ] – 1

= 1.224208 – 1 = 0.224208

= 0.2242 ( When rounded off to four decimal places )

= 22.42 %

Thus annualized rate of return for the T- bill = 22.42 %

NOTE : The value of ( 133.83 ) ^{( 1.3333 )}   has been calculated using the excel function =POWER(Number,Power). Thus =POWER(133.83,1.3333) = 1.224208