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# How the APY is Calculated

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.

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)

P = (Principle + Interest)

**= $100**A = (Total Accrued Amount)

**= $183,394.2**Last modified 9mo ago