Reverse compound or simple interest: find the starting principal from a final balance, or solve for the interest rate, number of periods or final amount.

Rate and periods must use the same time unit.

For monthly periods, enter a monthly rate.

Display options

Reverse Interest Formula

The compound-interest formula below finds principal P from accumulated balance A, decimal rate per period r and number of periods n.

P = A / (1 + r) n
  • Where P is the principal amount
  • A is the accumulated balance in the same currency as P
  • r is the interest rate per period (decimal)
  • n is the number of periods

Reverse Interest Definition

Reverse interest finds a starting principal from a final balance, a rate per period and elapsed periods. This calculator also solves for the rate, periods or final balance under compound or simple interest, using one starting amount and a constant rate.

Compound interest: A = P(1 + r)n; P = A / (1 + r)n; r = (A / P)(1 / n) − 1; n = ln(A / P) / ln(1 + r).

Simple interest: A = P(1 + rn); P = A / (1 + rn); r = (A / P − 1) / n; n = (A / P − 1) / r.

Use the rate for the same period unit as n: for a monthly rate, enter months; for an annual rate, enter years. Enter the rate as a percentage; the formulas use its decimal equivalent. Fractional periods use the selected mathematical model.

Principal and final balance must be positive, and elapsed periods must be nonnegative. Compound interest requires a rate above −100% per period. Negative simple-interest rates are valid while 1 + rn stays positive. A negative interest change means the balance decreased.

At zero periods, the final balance equals principal and the rate cannot be uniquely recovered. At a zero rate, equal principal and balance do not determine a unique period count; unequal amounts have no solution. With a nonzero rate, equal amounts imply zero elapsed periods.

Money decimal places control display only. Keep full calculation precision until formatting the result.

Example Problem

How to calculate reverse interest?

First, determine the accumulated amount. For this problem, over a term of 5 years, the accumulated amount is found to be $400,000.00.

Next, determine the interest rate per period. This is found to be 5% per year. This will be converted to a decimal of .05 for calculations.

Next, determine the total number of periods. As mentioned above, this is a time period of 5 years.

Finally, use the compound-interest principal formula for five annual periods at 5% per year.

P = A / (1 + r) n

= 400,000/ (1+.05)5

= $313,410.47