Search…
💸
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
Export as PDF
Copy link
On this page
Simple Interest Equation (Principal + Interest)
Simple Interest Formulas and Calculations:
Example: