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### To annualize is the process of converting a short-term figure into an annualized term so that it is easy to compare values and make informed decisions. Investors, borrowers, and companies who want to assess the efficiency or cost of various assets, securities, or loans can benefit from annualizing.

Investors can compare the returns of various assets with various time periods by annualizing. When comparing, for instance, a three-month Treasury bill with a 0.5% yield with a one-year bond with a 2% yield, investors can annualize the Treasury bill's return using the following formula:

**Annualized return**= (1 + periodic return) ^ (number of periods in a year) - 1

The annualized return on the Treasury bill in this situation is (1 + 0.005) 4 - 1 = 0.0201 or 2.01%. This indicates that if the investor reinvested the Treasury bill's principal and interest at the same rate every three months, they would have earned 2.01% in a full year. Investors may see that the Treasury bill delivers a slightly greater return by contrasting this with the bond's yield of 2%.

**APR**= [(total interest + fees) / loan amount] / (loan term in years)

In this instance, [(600 + 200) / 10,000] / 0.5 = 0.16, or 16%, is the APR. In other words, over the course of a year, the borrower pays interest and fees totaling 16% of the loan amount.

**EAC**= (initial cost x annuity factor) + annual operating cost

The annuity factor is calculated as:

**Annuity factor**= [interest rate / (1 - (1 + interest rate) ^ (-number of years))]

Assume that Machine A, which costs $10,000 and lasts for five years at a cost of $2,000 per year, and Machine B, which costs $15,000 and lasts for seven years at a cost of $1,500 per year each. Assuming an interest rate of 10%, the EACs of both machines are:

**EAC of machine A**= (10,000 x 0.2638) + 2,000 = $4,638

**EAC of machine B**= (15,000 x 0.2122) + 1,500 = $4,683

This means that Machine A has a lower annualized cost than Machine B over their lifetimes.