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APY Calculations
Calculating APY

Simple Interest Equation (Principal + Interest)

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.
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Simple Interest Formulas and Calculations:

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)
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Simple Interest Equation (Principal + Interest)
Simple Interest Formulas and Calculations: