Would You Rather Math: $100 Now or $10 Each Week?
Two offers. One clear set of rules. Use the totals to explain when each choice gives you more.
Here is a hypothetical math choice, not a real payment offer: would you rather receive $100 today or $10 at the end of each week for 12 weeks?
You do not receive a payment at the beginning of the weekly plan. Ignore interest, fees, spending, and investing; compare only the total money received. These details matter because changing the rules changes the comparison.
I want you to make a choice and show the evidence behind it. “The bigger number” is not a complete explanation until you say which number, at what point in time, and why.
I can use a table and an equation to compare two payment plans and justify when each total is larger.
- I follow the timing rules.
- I calculate both totals accurately.
- I identify when the totals are equal.
- I separate the final total from a preference about timing.
$100 today
You receive the entire $100 immediately. No more payments follow in this model.
$10 each week
You receive $10 at the end of each of 12 weeks. At the start, you have received $0.
Build the comparison before choosing
Copy the table and complete the blank totals. Use the number of completed weeks, not the number of calendar labels on a page.
| Completed weeks | Offer A | Offer B |
|---|---|---|
| 0 | $100 | $0 |
| 5 | $100 | ___ |
| 9 | $100 | ___ |
| 10 | $100 | ___ |
| 12 | $100 | ___ |
Let w represent completed weeks, from 0 through 12. Offer B has total B = 10w. Offer A has total A = 100 throughout this comparison.
Answer all three questions
- Which offer gives more money by the end of 12 weeks, and how much more?
- At the end of which week are the totals equal? When does Offer B first become larger?
- If the comparison ended after only 9 weeks, would your conclusion about the larger total change?
Then explain your preference. You may prefer immediate access to the $100 or the larger total after 12 weeks. A preference about timing is different from a calculation about the final amount. Your explanation should make that distinction visible.
Sentence frame: “By week ___, Offer ___ gives $___ more because ___. I would choose ___ under these rules because ___.”
Check the totals after making your argument
Offer B pays $50 after 5 weeks, $90 after 9 weeks, $100 after 10 weeks, and $120 after 12 weeks. The two totals are equal at the end of week 10. Offer B first becomes larger at the end of week 11, when it reaches $110.
By week 12, Offer B gives $20 more. If the comparison ended after 9 weeks, Offer A would give $10 more. The time period is part of the mathematics.
Change one rule and test again
New hypothetical plan: Offer B pays $8 at the end of each week for 12 weeks. Does it reach $100 during the plan? Explain without rounding the weekly payment.
Check the extension
After 12 weeks, 8 × 12 = $96, so it does not reach $100 during this plan. If the same payments continued, the total would first exceed $100 after 13 complete weeks: 8 × 13 = $104. But week 13 is outside the stated 12-week plan.
Before sharing, check your units and payment timing. If you counted a payment at week 0, revise the table using the rule that the first payment happens at the end of week 1. Use your notebook or the response space your teacher assigns.
For more comparisons and visual models, explore the math learning pathways. For a different type of challenge, visit the Brain Challenge.
12 Responses
By week 12, offer B gives $20 more because 10×12=120. I would choose offer B under these rules because it has more money than offer A.
I would rather have 10$ each week because if I say 100$ then I would only get 100$ but if I choose 10$ I would get 120$ at the end of the 12 weeks making it better than 100$ for one day.
I would rather choose $100 immediately. If I saved up the 10 dollars I got each week for 12 weeks, I would only have 20 more dollars in the end than if I just got 100 dollars immediately. I don’t see a reason to have it spread over 12 weeks.
Offer B gives more money by the end of 12 weeks, and it gives $20 more.The totals are equal at the end of week 10, and offer B first becomes larger at the end of week 11.The conclusion would change because offer A would be larger after 9 weeks.
At first I would pick getting 10 dollars each month but after the payment plan changes into 8 dollars a month I would pick getting 100 dollars instantly.
Totals received in the hypothetical plans
Completed weeks Offer A Offer B
0 $100 $0
5 $100 $60
9 $100 $108
10 $100 $120
12 $100 $134
By week 9, Offer B gives $108 more because You get 10 dollars a week instead of 100 dollars and no more payments. I would choose 10 dollars a week under these rules because in the in you get $134 and you get paid more.
I would rather have 10 dollars every week.By week 12, Offer B gives $20 more because it would give more money at the end of the 12 weeks. I would choose option B under these rules because it would give more money and at the end of the 12 weeks,because option A would only be $100 but option B would be $120. If it was only 9 weeks I would choose option A because A would be $100 and B would only be $90.
By week 10 I would have the same amount if I chose $100 right now. Offer B gives $20 more because at the end of the twelve weeks I would have $120. I would choose Offer B under these rules because I can wait 12 weeks just for $120.
If I were to have a choice of 10 dollars for 12 weeks or 100 dollars now i would choose 100 dollars now because if I were to have 10 dollars for 12 weeks it would 10 weeks to get 100 dollars and I would not wait that long.
Totals received in the hypothetical plans
Completed weeks Offer A Offer B
0 $100 $0
5 $100 $50
9 $100 $90
10 $100 $100
12 $ 100 $120
The offer 10 dollars each week gives you more money because it gives you $20 more.
At the end of week 10 the total is equal and offer B first becomes longer at week 12.
My conclusion about the larger total change is when at week 12 you have 120 and for offer A you only have 100.
By week 12, Offer B gives $20 more because you get 10 dollars each week instead of 100 and no more payments. I would choose offer B under these rules because you get $120 instead of just 100 and no more payments after it.
At week 9, A gives ten dollars more because it pays out more money faster in the early weeks. I would choose Offer A under the rules because having quicker access to the money early on is way better to me than waiting for a higher final total.
I would rather get $10 each week because it is better to have more money if I get $100 it will maybe be gone so I would rather get $10 each week.