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# How the APY is Calculated

### Simple Interest Equation (Principal + Interest)

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.

### Simple Interest Formulas and Calculations:

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:

A=P* POW((1 + rt),365)
r=0.0000817
t = 24* 12
P = (Principle + Interest) = \$1,000
A = (Total Accrued Amount) = \$4,860,136.6

### Actual compound interest by day:

Day 1：\$1023.5296
Day 2：\$1047.6128420762
Day 3：\$1072.2627532051
Day 4：\$1097.4926668829
Day 5：\$1123.3162303376
... ...
Day 361：\$4428400.0359306
Day 362：\$4532598.517416
Day 363：\$4639248.7474914
Day 364：\$4748408.4148204
Day 365：\$4860136.5654578