How the APY is Calculated

How the APY is Calculated

• 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)

Example:

P = (Principle + Interest) = $1,000

First, convert R as a percent to r as a decimal r = R/100 r = 0.0158/100 r = 0.000158 rate per EPOCH,

Then solve the equation for A A = Pert A = 1,000.00(2.71828)(0.000158)(52560) A = $4,041,939.78

Summary: The total amount accrued, principal plus interest, with compound interest on a principal of $1,000.00 at a rate of 0.0158% Per Epoch compounded continuously over 52560 EPOCH is $4,041,939.78.

A = (Total Accrued Amount) = $4,041,939.78