the time value of money

Imagine a friend offers to give you 100 dollars. Would you rather have it today, or one year from now? Almost everyone wants it today, and that instinct is exactly right. Money in your hand today is worth more than the same amount promised later, because you can spend it now, invest it to earn more, or simply rest easy knowing you actually have it. This simple truth — that the timing of a payment changes its worth — is what actuaries call the time value of money.

More precisely, money has a price for being borrowed or lent over time, and that price is interest. If a bank pays 5 percent a year, then 100 dollars today grows to 105 dollars in a year, so 100 dollars now and 105 dollars in a year are worth the same to you. Run that logic backwards and 105 dollars a year from now is worth only 100 dollars today. Comparing amounts at different dates therefore requires moving them all to a common point in time, either forward (accumulating) or backward (discounting), using an interest rate.

This idea is the foundation of every actuarial valuation. Insurance premiums are collected today to pay claims years or decades from now; pension contributions made by a 30-year-old must fund a benefit at age 65. You cannot simply add up cash flows that occur at different times — that would be comparing apples to oranges. The whole machinery of interest theory exists to put every payment on the same footing so that fair prices, reserves, and liabilities can be calculated honestly.