Credit cards, for example, may advertise monthly interest rates, like 1 or 2 percent, but they have to show borrowers the annualized rate when they sign credit contracts. This will be listed as the annual percentage rate, or APR, on the contract. [1] X Research source
For the purposes of calculating the annualized rate, you will have to know your period interest rate expressed as a decimal. You can find this value by dividing the stated period interest rate by 100. For example, 1 percent would be 1/100, or 0. 01.
Alternately, a bond payment may make semiannual interest payments. This would be 2 payment period per year.
For example if you were quoted a rate of 1 percent per month (r=0. 01, n=12), compounded annually, your annualized interest rate is 12∗0. 01=0. 12{\displaystyle 12*0. 01=0. 12} (or 12%). This calculation should be used if the rate compounds annually, rather than quarterly, monthly, or some other frequency.
Note that in order to calculate the annualized percentage, this number will have to be converted to decimal form. You can do this by dividing the stated period interest rate by 100. For example, a 1 percent period rate would be expressed as 0. 01 (1/100).
For example, a periodic yield of 1 percent compounded monthly would be calculated as ((1+0. 01)12)−1{\displaystyle ((1+0. 01)^{12})-1}. [4] X Research source
After adding these numbers (1 + 0. 01), your equation should look like this:((1. 01)12)−1{\displaystyle ((1. 01)^{12})-1} Solve the exponent. This is done by entering the lower number (1. 01 in this case), pressing the exponent button (which is usually xy{\displaystyle x^{y}}), entering the higher number (12) and pressing enter. The equation should now be: (1. 127)−1{\displaystyle (1. 127)-1} The result, 1. 127, has been rounded to make calculation simpler. Keeping more decimal places will make your calculation more accurate. Subtract the one. This gives: 0. 127{\displaystyle 0. 127}. Represented as a percentage, by multiplying by 100, this is 12. 7 percent. So, an interest rate of 1 percent compounded monthly gives an annual percentage rate of 12. 7 percent. [5] X Research source
For example, an investment with a value of $20,000 at the beginning of the year and $20,800 now would have a year return to date of $800 ($20,800-$20,000). [7] X Research source
For the previous example, this would be $800 (the year return to date) divided by $20,000 (the initial value), to get 0. 04. Multiply this number by 100 to get the percentage return, which would be 100*0. 04, or 4 percent. [8] X Research source
For example, if you are calculating these values at the end of August, this would mean that 8 months have passed in the current year. In this case, your time factor would be calculated as 12 divided by 8, which would give a time factor of 1. 5.
For the previous example, this number would be the percentage return, 4 percent, multiplied by the time factor, 1. 5, to get a 1. 5*4, or 6 percent, year-to-date return. So, for an investment with a value of $20,000 that has earned $800 up to the end of August, the annualized yearly return would be 6 percent.
