the time value of money (intro)

Would you rather have 100 dollars today or 100 dollars a year from now? Almost everyone picks today — and they're right. Money in hand can be invested to earn interest, it loses purchasing power to inflation while you wait, and a future promise always carries some chance of not being kept. So the same number of dollars is simply worth more the sooner you get it. This plain truth — that timing changes value — is the time value of money, and it underlies every long-term financial promise an actuary deals with.

The time value of money is the principle that a sum of money has a different value depending on when it is received or paid. Two operations express it. Accumulating moves money forward: 100 dollars invested at 5 percent grows to 105 dollars in a year, because PV times (1 + i) gives the future value. Discounting moves money backward: a 105-dollar payment due in a year is worth only 100 dollars today, found as 105 divided by (1 + i). Stretch it out and the effect compounds — 1,000 dollars promised in 20 years at 5 percent is worth only about 377 dollars today (1000 divided by 1.05 to the 20th power). The further off a payment, the more discounting shrinks its present value.

For actuaries this is not a curiosity but the backbone of the job. Insurance and pensions are promises to pay money years or decades hence, so every premium, reserve, and pension contribution must be expressed in today's terms by discounting expected future cash flows. The chosen interest (or discount) rate is therefore one of the most consequential assumptions an actuary makes: too high and the liability looks deceptively small, too low and it looks crushing. This entry is only a teaser — the precise mechanics of interest, discount, and annuities are developed in their own dedicated terms.