# How do I calculate my annual percentage yield?

I have an asset that I purchased at \$440K. 5 years later, I sell this asset at \$725K.

How do I compute the annual percentage yield that I have been getting over the past 5 years from this asset?

• Were there any dividends or payments given by the asset? By yield do you mean merely your annualized rate of return? – JB King Jun 28 '14 at 7:49
• Nope. No dividends. Just what I paid in for and what I got out with. – Calvin Cheng Jun 28 '14 at 7:56

Applying some simple Math:

\$725,000/\$440,000 = 1.6477272727272....

So, your cumulative return is 64.8% if I round to 3 digits.

Now, if I take the 5th root of 1.648, I get approximately 1.1050742047085970060712045917364

So, your annualized rate of return is 10.5%.

• Double rounding? – Chris Degnen Jun 28 '14 at 12:11
• @ChrisDegnen - I thought to comment on this as well. I've seen students using log tables that only have 2 significant digits and result in calculations concluding that 2^5 = 30. I tell them to round only the final result, not interim steps. – JTP - Apologise to Monica Jun 28 '14 at 14:28
• @JoeTaxpayer: especially since the unrounded intermediate result is just sitting there in your calculator, waiting to be 5th rooted. It's actually more work to round it... – DJohnM Jun 28 '14 at 15:43

A1 = A0 + rA0

A2 = A0 + rA0 + r(A0 + rA0) = A0 + 2rA0 + r^2A0 = A0(1 + r)^2

At = A0(1 + r)^t

r = (At/A0)^1/t - 1

r = (725/440)^1/5 - 1 = 10.5%

• Is someone out there allergic to simple algebra? – mistermarko Jun 28 '14 at 19:30
• Maybe if you put in some explanation it would help. – soakley Jun 29 '14 at 21:03