> For the complete documentation index, see [llms.txt](https://medusa-finance.gitbook.io/medusa/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://medusa-finance.gitbook.io/medusa/how-the-apy-is-calculated.md).

# How the APY is Calculated

### <mark style="color:green;">Simple Interest Equation (Principal + Interest)</mark>

A = P(1 + rt)

Where:

* A = Total Accrued Amount (principal + interest)
* P = Principal Amount
* I = Interest Amount
* r = Rate of Interest per year in decimal; r = R/100
* R = Rate of Interest per year as a percent; R = r \* 100
* t = Time Period involved in months or years

From the base formula, A = P(1 + rt) derived from A = P + I and since I = Prt 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 units such as months or years. Time conversions that are based on day count of 365 days/year have 30.4167 days/month and 91.2501 days/quarter. 360 days/year have 30 days/month and 90 days/quarter.

### <mark style="color:green;">Simple Interest Formulas and Calculations</mark> <a href="#simple-interest-formulas-and-calculations" id="simple-interest-formulas-and-calculations"></a>

A = the Final Investment Value, using the simple interest formula: A = P(1 + rt) where P is the Principal amount of money to be invested at an Interest Rate R% per period for t Number of Time Periods. Where r is in decimal form; r=R/100; r and t are in the same units of time.

The accrued amount of an investment is the original principal P plus the accumulated simple interest, I = Prt, therefore we have:

A = P + I = P + (Prt), and finally **A = P(1 + rt)**

* Calculate Total Amount Accrued (Principal + Interest), solve for A
  * A = P(1 + rt)
* Calculate Principal Amount, solve for P
  * P = A / (1 + rt)
* Calculate rate of interest in decimal, solve for r
  * r = (1/t)(A/P - 1)
* Calculate rate of interest in percent
  * R = r \* 100
* Calculate time, solve for t
  * t = (1/r)(A/P - 1)

### <mark style="color:green;">Example:</mark> <a href="#example" id="example"></a>

**P = (Principle + Interest) = $1,000**

**A = (Total Accrued Amount) = $3,830,258.00**


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