Savings challenge calculator: how much do the 52-week and 100 envelope challenges save?
The 52-week money challenge saves $1,378: $1 in week 1, $2 in week 2, up to $52 in week 52. The 100 envelope challenge saves $5,050: you number 100 envelopes from $1 to $100 and fill each one once. Both totals follow the same rule, the sum of 1 to n is n × (n + 1) ÷ 2. To reach your own goal, divide it by 1,378 or 5,050 and round up: that is your step. Example: a $2,000 goal over 52 weeks needs steps of $1.46, so week 52 costs $75.92.
Calculate your challenge
Pick a challenge and a step size, or enter a goal and let the calculator find the step. For the envelope challenge, say how many envelopes you fill each week.
Worked example
| Challenge | Step | Total | Hardest week |
|---|---|---|---|
| 52 weeks, $1 steps | 1.00 | 1,378.00 | 52.00 |
| 52 weeks, goal $2,000 | 1.46 | 2,011.88 | 75.92 |
| 100 envelopes, 2 per week | 1.00 | 5,050.00 | 199.00 |
| 100 envelopes, goal $2,000, 2 per week | 0.40 | 2,020.00 | 79.60 |
What the example shows: the classic 52-week challenge saves only $36 in its first eight weeks but $202 in its last four, and those fall in December if you start in January. The envelope challenge is bigger and less predictable: with two envelopes a week it takes 50 weeks and averages $101 a week, but the week you draw $100 and $99 costs $199.
How the numbers work
In the 52-week challenge, week n costs n steps, so after week n you have saved n × (n + 1) ÷ 2 steps. After 52 weeks that is 1,378 steps. The 100 envelope challenge is the same sum with 100 numbers: 5,050 steps. If you fill k envelopes a week in random order, you need 100 ÷ k weeks, rounded up; an average week is the total divided by that number of weeks. The worst week is the k highest envelopes at once.
Common mistakes
- Starting in January the normal way round. The largest deposits then land in December, next to holiday costs. Run the challenge in reverse, $52 first and $1 last, or start it in spring.
- Picking the $5,050 challenge on a $1,378 budget. With two envelopes a week, the envelope challenge needs about $440 a month on average. Check that number against your budget before you start.
- Leaving the money in envelopes. Cash at home is easy to borrow from. Move each week's amount to a savings account and mark the box as done.
- Quitting after a missed week. Pay the missed week together with the next one, or skip it and carry on. A challenge at 90% still beats no savings.
Follow-up questions
Is a savings challenge better than a fixed monthly amount? Not in money: $1,378 is $26.50 a week either way. The challenge helps if a small start and a chart you color in keep you going. If you save for a fixed bill, our sinking funds calculator gives you the exact monthly amount instead.
What should the money go towards? If you do not have one yet, an emergency fund first. Our emergency fund guide works out the size.
Disclosure: Still Penny makes the Savings Challenge Printable (3.90 EUR, one-time purchase on Etsy): the 100 envelope challenge, the 52-week challenge with running totals, a blank 52-week plan and coloring charts for $1,000, $5,000 or your own goal, as PDF in US Letter and A4. It is optional: the calculator above is free.
General information, not financial advice.