# APY Calculations

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

**A = P\*(1 + r\*T)**

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, <mark style="color:purple;">A = P(1 + rt)</mark> derived from <mark style="color:purple;">A = P + I</mark> and since <mark style="color:purple;">I = Prt</mark> then <mark style="color:purple;">A = P + I</mark> becomes <mark style="color:purple;">A = P + Prt</mark> which can be rewritten as <mark style="color:purple;">A = P(1 + rt)</mark>

**Note that rate r and time t should be in the same time units such as months or years.**&#x20;

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:blue;">Simple Interest Formulas and Calculations:</mark>

A is the Final Investment Value, using the simple interest formula: <mark style="color:purple;">A = P(1 + rt)</mark>&#x20;

P is the Principal amount of money to be invested at an Interest Rate R% per period for t Number of Time Periods. &#x20;

Where r is in decimal form; <mark style="color:purple;">r=R/100</mark>; 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, <mark style="color:purple;">I = Prt</mark>, therefore we have:

<mark style="color:purple;">A = P + I = P + (Prt)</mark>, 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)**


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