Time Value of Money

One dollar, three reasons to want it now

Offered $1,000 today or $1,000 in five years, take it today. The deepest reason is productive: money in hand can be put to work. Invested at even a modest return, today's $1,000 grows into more than $1,000 by the time the later payment would arrive, with compound interest doing the heavy lifting. The gap between the two offers is not a feeling; it is the return you could have earned in between.

Inflation supplies the second reason. Prices tend to drift upward, so a dollar delivered years from now buys less than a dollar delivered today. Even if you never invested a cent, waiting quietly shrinks what the money is worth in groceries, rent and everything else.

Uncertainty supplies the third. A promise of future money can be broken: the payer can fail, the terms can change, life can intervene. A dollar today is certain in a way no future dollar can be, and certainty is worth something. Put the three together and time itself has a price, and that price is the interest rate.

Two directions, two names

The time value of money is one idea driven in two directions, and each direction has its own name. Travel backwards, shrinking a future amount into today's terms, and you are computing present value. Travel forwards, growing today's money into what it will become, and you are computing future value. Same machine, opposite gears; both articles walk through the formulas, so there is no need to repeat them here.

What matters at this altitude is what the machine lets you do: compare money across time on fair terms. $10,000 today and $14,000 in six years cannot be compared directly, any more than kilometres and miles can. Discount both to today, or grow both to the same future date, and suddenly they are in the same unit and the better offer is plain. For a quick mental shortcut on growth, the rule of 72 estimates how long money takes to double at a given rate.

Where the principle quietly decides real choices

The time value of money rarely announces itself, but it sits underneath several decisions Canadians actually face:

• The pension decision. Leaving a job with a defined benefit pension often means choosing between monthly payments for life and a lump-sum commuted value. The lump sum is nothing more than your future payments discounted to today, so the choice is a pure time-value comparison dressed up in retirement paperwork.
• Pay off the mortgage or invest. Every extra mortgage payment "earns" your mortgage rate, guaranteed. The same dollar invested might earn more, might earn less. You are weighing two futures for one present dollar, which is the time value of money in street clothes.
• Lump sum or annuity. A lottery prize paid as $1,000 a week for life and its single-cheque alternative are the same prize quoted at different dates. Only discounting both to today reveals which one is actually richer.
• "No payments for 12 months." Deferred-payment financing is the principle working against you. The delay has a cost, and it is built into the price, the fine print, or both; many such contracts charge interest back to day one if the balance is not cleared on time. Nobody defers your payment out of generosity.

Opportunity cost: the everyday face

You do not need a formula to use the time value of money daily; you need the habit of asking what else the dollar could be doing. That habit has a name: opportunity cost. Every dollar spent, lent or left idle has an alternative use, and the return on the best alternative is the real cost of the choice you made. Money parked in a chequing account earning nothing is not "safe from decisions"; it is a decision, one that pays 0% while inflation works on it.