What is the formula for annualised return for investment?

Question

Example if an investment increases in value in a two-year period from $100 to $125. The increase of $25 in the two-year period would represent a cumulative return of 25%. But how would you calculate the annualised return ?

Answer 1

You should provide more detail in your question.

Are you talking about the APR given a periodic yield or a holding period return? If period, then how many compounding periods in the period?

Let's look at a couple of examples. Suppose that you are told that the yield of a US treasury bond is 5%. What is the APR. Treasury bonds compound semiannually. This means that you get 2.5% per half year. The APR is:

(1+y/2)^2 - 1 = 1.025^2-1 = 5.062%

Supose you are told that your morthage rate is 8%. Mortgages compound monthly, so your monthly rate is 0.667% per month and the APR is:

(1+M/12)^12-1 = (1+.08/12)^12-1 = 8.3%

Here is a tricky one. Suppose you put money into a checking account at 4%. This compounds daily -- but at a rate equal to the stated rate divided by 360 (not by 365). So, the APR is:

(1+R/360)^365 = (1+.04/360)^365 = 4.139%