Annuity Future Value

Compound interest is exponential, not linear. In a 30-year retirement plan, roughly half the total balance accumulates in the final 10 years. This is why starting early matters so much more than contributing more later — the base on which interest compounds is much larger after 20 years of growth. Doubling your deposit at year 25 helps far less than starting 5 years earlier would have.

An annuity is simply a stream of equal deposits made at regular intervals — monthly, quarterly, or yearly. This tool adds them up while every past deposit keeps earning on its own, then splits the final balance into two parts: the money you put in (blue line) and the growth it generated (green shading). The takeaway: once the green balance line pulls clearly away from the blue contributions line, most new money is coming from returns, not from your wallet.

The engine here is a geometric series: FV = d·((1+r)ⁿ − 1)/r. Swap the growth factor (1+r) for a shrinking one and you get the exact equation pharmacologists use for repeated drug doses. Because each deposit grows while each drug dose decays between intervals, an annuity climbs without limit while blood concentration levels off at a steady-state plateau — same equation, opposite destiny, decided only by whether the ratio sits above or below 1.