The simple interest formula
Simple interest is calculated by multiplying three variables: the principal (the original amount), the annual rate expressed as a decimal, and the time in years. The result is the total interest earned or owed over that period. Adding the interest to the principal gives the total amount at the end of the term.
For example, 1,000 invested at a 5% annual simple interest rate for 3 years earns 1,000 × 0.05 × 3 = 150 in interest, giving a total of 1,150 in the same currency. No matter how long the term extends, the interest earned each year stays fixed at 50 because simple interest always applies to the original principal, never to accumulated interest.
The effective annual yield — interest earned per year as a percentage of the principal — equals the annual rate under simple interest, because the annual interest amount is constant. This differs from compound interest, where the effective annual yield increases over time as interest earns further interest.
I = P x r x t
I is the interest earned, P is the principal, r is the annual interest rate as a decimal, and t is the time in years.
A = P + I = P x (1 + r x t)
A is the total amount at maturity, combining the original principal and the accumulated interest.
P = I / (r x t)
Rearranging the formula lets you find the principal needed to earn a target interest amount at a given rate and term.