$1,000 now or $1,100 later? Now wins.
The story so far The bike shop had a great year, and the owner offers you a bonus. You can take $1,000 today, or $1,100 in 2 years. $1,100 looks bigger. But your savings account pays 5% a year. Put the $1,000 in today and in 2 years it grows to $1,102.50, more than $1,100. Money you have now can start earning right away. That's the time value of money, and it's behind every loan, investment, pension and lottery payout.
A dollar today is worth more than a dollar later, because today's dollar can earn interest in the meantime.
It lets you compare money at different times: a bonus now or later, a lump sum or payments, a car loan or cash.
Move every amount to the same moment. Grow today's money forward, or shrink future money back to today.
Corporate finance analysts use it to decide which projects to fund. Bankers price loans with it. Financial planners use it to compare pension and payout choices.
What you're looking at: the $1,000 bonus taken today and saved at 5% a year. After 1 year it's $1,050; after 2 years, $1,102.50. The dashed line is the $1,100 you'd get by waiting. Taking the money now ends up $2.50 ahead.
Moving money through time.
To compare amounts at different times, bring them to the same moment. You can go forward (future value) or back (present value). It's the same math, run in opposite directions.
Why a dollar now beats a dollar later
The time value of money comes from three things. Money now can earn interest. Inflation (Lesson 9.1) makes later dollars buy less. And a promise of money later has risk: it might not arrive.
- Your bonus
- The $1,000 today can sit at 5% for 2 years. The $1,100 can't earn anything until you get it.
Future value: growing money forward
Future value is what today's money grows to. It's the compound growth formula from Lesson 10.1.
- $1,000 today at 5%
- $1,000 × 1.05 × 1.05 = $1,102.50 in 2 years. That's the future value.
Present value: shrinking money back
Present value runs the math in reverse: how much a future amount is worth today. Turning future money into today's money is called discounting.
- $1,100 in 2 years at 5%
- $1,1001.05 × 1.05 = $1,1001.1025 = $997.73 today. That's less than $1,000, so taking the money now wins.
The discount rate
The rate you use is the discount rate: what you could earn on the money elsewhere. It's an opportunity cost (Lesson 8.1). The higher the rate, or the longer the wait, the less future money is worth today.
- $1,100 in 2 years, at 5%
- Worth $997.73 today.
- Same, at 2%
- $1,1001.02 × 1.02 = $1,057.29 today. With a lower rate, waiting would win.
A stream of payments
Many deals pay a set amount every year, like a pension or a lottery payout. A stream of equal payments is called an annuity. Its present value is just the present value of each payment, added up.
- $100 a year for 3 years, at 10%
- $1001.10 + $1001.102 + $1001.103 = $90.91 + $82.64 + $75.13 = $248.69 today, not $300.
What you're looking at: the $1,000 bonus now against a later offer you set. Both bars are in today's dollars: the second bar is the later offer discounted back to today. Whichever bar is longer is the better deal.
Two minutes. Just listen.
Tap any line to jump to it.
Now or later?
Eight offers. Each one gives you the numbers. Work out what each choice is worth at the same moment, then tap your answer. One try each.
What you're looking at: made-up offers. Each lists the amounts, the wait and the rate you could earn, then asks one question.
The logic, step by step.
Every now-or-later question takes the same three steps.
Step 1: Pick the rate
- Your savings account
- 5% a year.
Step 2: Move both amounts to the same moment
- Both to today
- $1,000 stays $1,000. $1,1001.1025 = $997.73.
- Or both to year 2
- $1,000 × 1.1025 = $1,102.50. $1,100 stays $1,100.
Step 3: Compare
- Either way
- Now wins by $2.27 in today's dollars, or $2.50 in year-2 dollars. Same answer.
Worked example: when does waiting win?
- The question. How big would the 2-year offer need to be to beat $1,000 now?
- The rate. 5% a year, your savings account.
- Grow $1,000 forward. $1,000 × 1.05 × 1.05 = $1,102.50.
- The answer. Any offer over $1,102.50 in 2 years beats $1,000 now. At exactly $1,102.50 they're worth the same.
- The lesson. "Bigger later" only wins if it's bigger by more than the money could earn in the meantime.
Squirrels know.
Gray squirrels treat acorns differently depending on how well they keep. White oak acorns sprout soon after they fall, so they lose value fast. Squirrels tend to eat those right away. Red oak acorns stay dormant until spring, so they hold their value. Squirrels are more likely to bury those for winter.
What you're looking at: an illustration, not data. A squirrel with white oak acorns on the left, which it tends to eat now, and red oak acorns on the right, which it tends to bury for winter.
Why this sticks. Whether to wait depends on what holds its value over time. Money in savings keeps growing, so saving it works. A promise that loses value while you wait, like a later payment in an inflation-heavy year, is worth less than it looks.
The page you'd copy down.
- Time value of money: a dollar now beats a dollar later (interest, inflation, risk).
- Future value = today × (1 + rate)years. $1,000 at 5% for 2 years = $1,102.50.
- Present value = future amount(1 + rate)years. $1,100 in 2 years at 5% = $997.73.
- Discount rate = what you could earn elsewhere. Higher rate or longer wait → lower present value.
- Annuity: add up the present value of each payment. $100 a year for 3 years at 10% = $248.69.
- To compare: move every amount to the same moment, then pick the bigger one.
Fill in the blanks
Grab a friend or a study group.
Would you wait?
Each person says the smallest amount in 1 year they'd take instead of $100 today. Compare your answers with what a 5% rate says: $105.
Break the tie
Use the slider above. One person sets the later offer; the other finds the rate where now and later are worth the same.
Lottery debate
Lump sum or yearly payments? Argue both sides, then check the math in the job task below.
Just you and your money.
These stay on this device. Nobody else sees them.
Exam-style questions.
Written the way a college exam would ask them. Each right answer on the first try is worth 10 xp.
On the job: you're a financial planner
Your client just won the lottery. They must pick one way to be paid:
- Lump sum: $600,000 today.
- Payments: $50,000 a year for 20 years, $1,000,000 in total.
- Present value of the payments at 5%: $623,111.
- Present value of the payments at 7%: $529,701.
Your task: which choice is worth more today if your client can earn 5% a year? What if they can earn 7%? Why isn't $1,000,000 the real value of the payments?
See a model answer
At 5%: the payments are worth $623,111 today, more than the $600,000 lump sum. Take the payments, by $23,111.
At 7%: the payments are worth $529,701 today, less than $600,000. Take the lump sum, by $70,299.
Why not $1,000,000: most of the payments arrive years from now. Each one is discounted back to today, and the last ones shrink the most.
The real question: what can your client actually earn, and will they invest the lump sum or spend it? Taxes also matter, so a tax pro should check the final numbers.
Every money choice has a clock.
What you're looking at: a map of where this lesson fits in the course. Read it left to right: the lessons it builds on, this lesson in the middle, and the lesson that comes next.
- Back · Unit 10The math of percent and growth
- Back · Unit 3Make your savings earn more
- Back · Unit 8Every choice has a price tag
- You are hereThe time value of money
- Next · Unit 10Money psychology