How much is $0.01 doubled everyday for 30 days?

If day 1 is one cent and the amount doubles every calendar day, day 30 is $5,368,709.12. The sum of all 30 days is $10,737,418.23.

Day n is $0.01 × 2^(n−1). Day 30 is $0.01 × 2^29. 2^10 is 1,024, so 2^20 is 1,048,576 and 2^29 is 536,870,912. Times one cent is $5,368,709.12. The sum of a doubling series from day 1 through day 30 is $0.01 × (2^30 − 1) = $10,737,418.23. This is arithmetic. It is not a savings account, not a return the market owes you, and not a plan.

Anyone selling a product “that works like the penny” is using the riddle as a sales pitch. Real doubling every day for a month would require a rate no deposit product pays. Compare an actual offer with the rate printed by the bank or, in Brazil, with the Tesouro Direto simulator — and do not import this dollar riddle into that simulator.

Sources

• The result is the closed form of a finite geometric series. No market data is involved.
• Tesouro Direto for anyone who arrived here looking for a real rate.

This note is educational. It is not a recommendation to buy, borrow or insure anything, and it promises no return.