effective rate of interest

When someone says an account earns 6 percent, you want to know one honest thing: if I leave one dollar in for exactly one year, how much extra do I have at the end? That single, no-tricks figure is the effective rate of interest. It already bakes in any compounding that happened during the year, so it tells you the true growth over the period rather than a quoted label.

Formally, the effective rate of interest for a period, written i, is the interest earned over that period divided by the balance at the start of the period: i = (amount at end minus amount at start) divided by amount at start. It is measured at the end of the period and stated as a fraction of the beginning balance. Under compound interest the effective rate stays the same period after period, which is exactly why a single number, i, can describe the whole accumulation: one dollar grows to (1 + i) raised to the power n after n periods.

The effective rate is the actuary's reference point because it is unambiguous: two investments can be compared fairly only after both are expressed as effective rates over the same period. A loan advertised at a low nominal rate but compounded monthly may have a higher effective rate than it appears, which is why consumer-protection laws often require lenders to disclose an effective annual figure. Whenever a problem gives you a rate without saying otherwise, it usually means the effective rate per period.