Compounding Interest Calculation

The Compounding Interest Formula
To calculate accrued amount Principal + Interest
A=P(1+r/n)ntA = P(1+r/n)^{nt}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)ntP = A/(1+r/n)^{nt}P=A/(1+r/n)nt
Calculate principal amount Solve for P in terms of I
P=I/((1+r/n)nt−1)P = I/((1+r/n)^{nt}-1)P=I/((1+r/n)nt−1)
Calculate the rate of interest as a decimal
r=n((A/P)1/nt−1)r=n((A/P)^{1/nt}-1)r=n((A/P)1/nt−1)
Calculate the rate of interest as a percent
R=r∗100R=r*100R=r∗100
Calculate time Solve for t 
(ln is the natural logarithm)
t=ln(A/P)/n(ln(1+r/n))t=ln(A/P)/n(ln(1+r/n))t=ln(A/P)/n(ln(1+r/n))
then also
t=(ln(A)−ln(P))/n(ln(1+r/n))t=(ln(A)-ln(P))/n(ln(1+r/n))t=(ln(A)−ln(P))/n(ln(1+r/n))
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Last modified 10mo ago

Compounding Interest Calculation

The Compounding Interest Formula

To calculate accrued amount Principal + Interest

Calculate principal amount Solve for P in terms of A

Calculate principal amount Solve for P in terms of I

Calculate the rate of interest as a decimal

Calculate the rate of interest as a percent

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