Published on

How to calculate APY (annual percentage yield)

Authors
  • avatar
    Name
    Benton Li
    Twitter

The equation is straightforward

APY=(1+iN)N−1APY = (1+\frac{i}{N} )^N -1

where:

i = stated rate

  • e.g. for a bond with principal of $1000 and monthly coupon of $5, i = $5 / $1000 * 12 (month) = 6%

N = number of compounding periods per year

  • if it’s compounded annually, N = 1
  • if it’s compounded monthly, N = 12

What does APY tell you?

For every dollar you invest, after x years, you get $1 * (1+APY%)n(1 + APY\%) ^ n.

For example, if you invest $100 now. After 3 years, you get $100 * (1+APY%)3(1 + APY\%) ^ 3.

How does APY actually make sense?

Say your bond’s face value is $100 now, a year later, the amount of interest you earn on the principal is $i. But this $i is not given to you at once, but N times throughout the year. And this $i is not the only interest you get either. You will also get “interests on interests“ — interests are compounded.

Example:

Suppose a bond’s face value is $100, the stated rate is 10%, and you get paid semiannually.

Then, i = 10%, N = 2.

After 6 months, you get interest based on $100, which is $100 * 10% / 2= $5. In the next paying period, interest will be calculated based on 100 + 5 = 105

After another 6 months, you get interest based on $105, which is $105 * 10% / 2= $5.25

Together with the principal, you get $100 + $5 + $5.25 =$110.25

Your APY will be ($110.25 - $100) / $100 = 10.25%

Using formula: APY = (1+10%/2)2−1(1+10\%/2) ^ 2 - 1 = 10.25%

Read more: