time value of money
/ T-V-M /
Suppose someone offers to give you $1,000 today or the same $1,000 in five years. Almost everyone takes it today, and they are right to. Money in your hand now is worth more than the identical amount promised later. This simple truth — that a dollar today beats a dollar tomorrow — is the time value of money, and it sits at the foundation of nearly all of finance.
Why is today's money worth more? Three reasons. First, you could invest it and earn a return, so $1,000 now could grow to more than $1,000 by year five (this is compound interest working for you). Second, prices tend to rise, so the same money buys less in the future (inflation). Third, the future is uncertain — a promise might not be kept. To compare amounts of money that arrive at different times, finance converts them to a common date. Pushing money forward in time (finding what it grows into) is compounding; pulling future money back to today (finding what it is worth now) is discounting. The interest rate is the price that links the two.
The time value of money is the reason interest exists at all, the reason loans charge more than they lend, and the reason a $1 million lottery paid over 20 years is worth far less than $1 million in cash. It is also why you cannot simply add up cash flows that arrive in different years — a profit of $100 next decade is not the same as $100 now. Every serious decision about saving, borrowing, investing, pensions, or valuing a business rests on first putting money on a common timeline.
A lottery advertises a $20 million jackpot paid as $1 million a year for 20 years. At a 5% interest rate, those future payments are worth only about $12.5 million today — which is why winners who take the lump sum receive far less than the headline figure. The missing $7.5 million is the time value of money.
Spreading the same dollars over future years lowers what they are worth today.
The time value of money does not depend on inflation alone. Even with zero inflation, money today is worth more, because it can be invested to earn a return. Inflation simply adds to the gap.