It is important for an investor to know how to calculate the annualized returns on his investments. Most brokerage firms and mutual and companies will provide you your investment summary and performance summary on a monthly basis, and the returns mentioned in them will most likely be monthly returns, not annual returns. Unless you annualize the returns, you will not have a clear idea of how your investment has performed, especially when there are some good months and some bad months.

So, let’s look at how you can annualize your monthly returns.

If you know the monthly rate, which is the same in all months, all you need to do is calculate the annualized returns using the following formula: APY = (1 + R)^12-1

So, if the monthly rate is 2% for all months, the annualized rate is:

= (1+2%)^12 – 1

= 1.02^12-1 = 0.2682 or 26.82%

If, on the other hand, you have monthly returns for separate months, then you will annualize the returns using the following formula:

APY = (1+r_{1})*(1+r_{2}) *(1+r_{3}) *(1+r_{4}) *(1+r_{5}) *(1+r_{6}) *(1+r_{7}) *(1+r_{8}) *(1+r_{9}) *(1+r_{10}) *(1+r_{11}) *(1+r_{12}) – 1

Let’s say the twelve monthly returns are 2%, 2.2%, 2.1%, -1.5%, 2%, 2.4%, 1%, -1.2%, -0.5%, 0.7%, 1%, and 1.5%.

Using the above monthly returns, we can calculate the annualized returns as follows:

APY = (1.02)(1.022)(1.021)(0.985)(1.02)(1.024)(1.01)(0.988)(0.995)(1.007)(1.01)(1.015) – 1

**Annualized return = 0.1223 or 12.23%**

Note that when the monthly return is positive (such as 2%), it is express as (1+2%) or (1+0.02) or (1.02). When the monthly return is negative (such as -1.5%), it is expressed as (1-1.5%) or (1-0.15) or (0.985).

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