First, let's get our vocabulary straight. What we are really talking aboutmathematicallyis rate of change; in mathematical terms, an interest rate is merely one example of a rate of change. When a rate of change is positive, it is also frequently called a rate of growth.

The mathematically correct formula for figuring out what the overall rate of change over n periods will be on the assumption that the rate of change for the first period remains constant over the next n - 1 periods is:

$(1 + z)^n -1,$ where z is the rate of change for the first period.

However, $if\ |z| \approx 0\ and\ n \le 12,\ (1 + z)^n -1 \approx n * z.$

Let's see how the approximation works for z = 0.25% and n = 12.

The answer using the correct formula is $(1 + 0.0025)^{12} - 1 = 1.0025^{12} - 1 \approx 1.0304 - 1 = 0.304 = 3.04\%.$

The answer using the approximation formula is $12 * 0.0025 = 0.03 = 3.00\%.$

For many practical purposes, the approximation formula is just as reliable as the correct formula.