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# APY Calculations

Calculating APY

**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, 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.

A is the Final Investment Value, using the simple interest formula: A = P(1 + rt)

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)**

Last modified 10mo ago