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Interest formula

Simple Interest Accumulation Function

For simple interest, the accumulation function grows linearly because interest is calculated on the original principal rather than on previously earned interest.

Core formulaa(t) = 1 + rt, so an initial principal P grows to A(t) = P(1 + rt).

The accumulation function

a(t) = 1 + rt
A(t) = P(1 + rt)

P is the original principal, r is the simple annual interest rate as a decimal, and t is time in years. The accumulation factor a(t) tells you how many dollars the investment or balance grows to for each dollar of principal.

Worked example

For $6,000 at 8.35% simple annual interest for 50 days using a 365-day year, t = 50/365. The interest is P × r × t, and the accumulated amount is principal plus that interest.

Simple Interest CalculatorCalculate principal, interest, and accumulated amount using days, months, or years.Daily Interest CalculatorCalculate per-diem interest using 360, 365, or 366-day bases.Compound Interest CalculatorCompare simple linear growth with compounding.Daily vs. Monthly InterestCompare daily accrual with monthly periodic calculations.

Simple interest vs. compound interest

Simple interest has a linear accumulation function because the interest base stays at the original principal. Compound interest has an exponential accumulation function because prior interest becomes part of the balance that earns future interest.