💸

# APY Calculation

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)*derivated 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 expressed in the same time unit, 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), solving A
- A = P(1 + rt)

- Calculate Principal Amount, solving P
- P = A / (1 + rt)

- Calculate rate of interest in decimal, solving r
- r = (1/t)(A/P - 1)

- Calculate rate of interest in percent, solving R
- R = r * 100

- Calculate time, solving t
- t = (1/r)(A/P - 1)

**P = (Principle + Interest) =**

**$1,000**

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

**$3,903,447.60**

****

Last modified 6mo ago