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# How to calculate APY (annual percentage yield)

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- Name
- Benton Li

**The equation is straightforward**

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 * $(1 + APY\%) ^ n$.

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

**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 = $(1+10\%/2) ^ 2 - 1$ = **10.25%**

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