Compounding Interest Calculation

## The Compounding Interest Formula

### To calculate accrued amount Principal + Interest

$A = P(1+r/n)^{nt}$
Where:
• A = Accrued amount (principal + interest)
• P = Principal amount
• r = Annual nominal interest rate as a decimal
• R = Annual nominal interest rate as a percent
• r = R/100
• n = number of compounding periods per unit of time
• t = time in decimal years; e.g., 6 months is calculated as 0.5 years. Divide your partial year number of months by 12 to get the decimal years.
• I = Interest amount
• ln = natural logarithm, used in formulas below
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.

### Calculate principal amount Solve for P in terms of A

$P = A/(1+r/n)^{nt}$

### Calculate principal amount Solve for P in terms of I

$P = I/((1+r/n)^{nt}-1)$

### Calculate the rate of interest as a decimal

$r=n((A/P)^{1/nt}-1)$

### Calculate the rate of interest as a percent

$R=r*100$

### Calculate time Solve for t (ln is the natural logarithm)

$t=ln(A/P)/n(ln(1+r/n))$
then also
$t=(ln(A)-ln(P))/n(ln(1+r/n))$