Compounding Interest Calculation

The Compounding Interest Formula

To calculate accrued amount Principal + Interest

A=P(1+r/n)ntA = 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}

Calculate principal amount Solve for P in terms of I

P=I/((1+r/n)nt1)P = I/((1+r/n)^{nt}-1)

Calculate the rate of interest as a decimal

r=n((A/P)1/nt1)r=n((A/P)^{1/nt}-1)

Calculate the rate of interest as a percent

R=r100R=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))
then also
t=(ln(A)ln(P))/n(ln(1+r/n))t=(ln(A)-ln(P))/n(ln(1+r/n))
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Outline
The Compounding Interest Formula