# Are divisions of returns linear?

If I have an annualized 5% return on \$2,000, which is \$100, can I always say that each 1% is \$20?

If that is the case, then this linear division of an annualized returns can be applied to more complex scenarios. For example, you buy an option requiring \$500 and hold it for 60 days, netting \$30. That's 6% on the holding period and 36% (12/2 x .06) annualized. Each annualized 6% in that case is \$5 right?

• Rates of return are always compounded. – RonJohn Aug 31 '19 at 15:14
• Simple math says that \$20 is 1% of \$2,000. You learned that in grade school. As for your second paragraph: after that sixty days, would you buy another \$500 option, netting \$30? And sixty days later, buy another \$500 option, netting \$30? – RonJohn Aug 31 '19 at 16:31
• This looks like what’s called an X-Y problem: you really want to know X, but you’re asking about Y. In this case, Y is a simple division: 100/5=20. What is your underlying question (the X)? Are you trying to work out, for example, the expected gain from a short-duration transaction, given an expected annualised yield? – Lawrence Aug 31 '19 at 17:15