> For the complete documentation index, see [llms.txt](https://eggplus.gitbook.io/welcome-to-gitbook/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://eggplus.gitbook.io/welcome-to-gitbook/how-it-works/fixed-apy/how-is-apy-calculated.md).
# How is APY calculated
### Simple interest equation (principal + interest)
A = P(1 + rt)
#### where:
A = total accrued amount (principal + interest)
P = principal amount I = interest amount
r = annual interest rate (decimal); r = R/100
R = interest rate percentage per annum; R = r \* 100
t = time period involving month or year
According to the basic formula, a = P (1 + rt) is derived from a = P + I, because I = Prt, and then a = P + I becomes a = P + Prt, which can be rewritten as a = P (1 + rt)
Note that rate R and time t should be in the same time unit, such as month or year. The time conversion based on 365 days / year has 30.4167 days / month and 91.2501 days / quarter. 360 days / year has 30 days / month and 90 days / quarter.
### Simple Interest Formula and Calculation:
A = final investment value, using a simple interest formula: A = P (1 + rt), where p is the principal amount invested at the interest rate R% of each period in t time periods. Where R is decimal form; r=R/100; r and t are in the same time unit.
The accrued amount of an investment is the original principal P and accumulated simple interest, I = Prt, so we have:
A = P + I = P + (Prt), lastly A = P (1 + rt)
Calculate the total accrued amount (principal + interest) and solve A
A = P(1 + rt)
Calculate the principal and solve P
P = A / (1 + rt)
Calculate the interest rate in decimal system and solve r
r = (1/t)(A/P - 1)
interest rate is calculated as a percentage
R = r \* 100
Calculation for T
.t = (1/r)(A/P - 1)
#### **Example:**
P = (principal + interest) = **$1000**
A = (total accrual) = **$**1,832,940