Time value of money
The idea that a dollar today is worth more than a dollar in the future because today's dollar can earn a return.
FV = PV × (1 + r)^t and PV = FV ÷ (1 + r)^t
Explanation
The time value of money says that when you receive money matters, not just how much. A dollar today can be saved or invested to earn interest, so it grows into more than a dollar later. Turned around, a dollar promised years from now is worth less than a dollar today, because you give up the growth you could have earned in the meantime.
Two other forces push in the same direction. Inflation erodes what a future dollar can buy, and there is always some risk that a promised future payment does not arrive. Together, growth, inflation and risk are why future money is “discounted” when you compare it with money today.
The app uses this idea everywhere. When a scenario grows your balances, it moves money forward in time (future value). When it asks how much you need today to fund spending later, it moves money backward (present value). Comparing options with different timing, such as paying off a loan versus investing, only works if all the dollars are expressed at the same point in time.
Example
Suppose you can earn 5% a year and someone offers you either $1,000 today or $1,050 in one year.
- Moving today’s money forward: $1,000 × 1.05 = $1,050 in one year.
- Moving the future money back: $1,050 ÷ 1.05 = $1,000 today.
The two offers are equal at 5%. If you could earn more than 5%, taking the $1,000 now is better. If the best you can do is 3%, then $1,050 ÷ 1.03 = $1,019.42 in today’s dollars, so waiting for the $1,050 is better.
Stretch it out: at 5%, $1,000 today grows to $1,000 × 1.05^10 = $1,628.89 in ten years. A promise of $1,628.89 in ten years is therefore worth only $1,000 to you today.