APR, APY and annualized return

[ammer.jens]

Hello, I am slightly confused regarding the APR, APY and the annualized return based on an exact number of days.

Assuming a starting balance of 10.000 USD after 1500 days (approx. 4.1 years) the balance increased to 35.000 USD. This is an increase of 250%. I calculate the exact (based on 1500 days) annualized return as follows:

(1+250%)^(365/1500)-1=36%

Is it correct that the APR would be the 250% and the APY would be the 36% ?

[Fernando Carreiro]

APR vs. APY: What’s the Difference

[ammer.jens]

Hi Fernando, thank's for your comment and the provided website. I have read that one already but couple of minutes ago I found this website:

https://finance.zacks.com/convert-simple-returns-equity-annualized-returns-1563.html

It is basically a step by step explanation of my formula provided above but in years and not based on exact days but you only have to replace the part at which you divide 1 by the number of years with 365/Number of days and you get your 36%.

HOWEVER, I think this calculated annualized return based on a total percentage increase is different from the APY as for the APY you expect to receive interest on a daily, weekly, monthly or yearly basis which you don't have when you just invest in a stock and hold it for a couple of months or years.