Separate income and withdrawal
Let B be the balance at the start of the month, i the monthly rate and W the withdrawal at month-end. New balance is B × (1 + i) − W. If withdrawal exceeds credited income, the difference comes from principal. The next month’s base is smaller, so the same rate credits less money. A fixed withdrawal is not a fixed share of income; as the balance falls, its burden relative to capital rises. Dividing the initial amount by the payment is valid only in a no-income, no-other-movement model.
A reproducible example
The fictional starting amount is 600,000 roubles, the fixed educational rate is 0.4% per month and the month-end withdrawal is 30,000. There are no taxes or costs. Month one credits 2,400 and leaves 572,400 after payment. Month two credits 2,289.60 and leaves 544,689.60. Month three credits about 2,178.76 and leaves about 516,868.36. The balance falls even though positive interest is credited. The 30,000 withdrawn cannot all be called interest income.
After the twentieth withdrawal, approximately 26,511.91 roubles remain. The next full payment is not funded in the stated model. The algebraic zero occurs at about 20.89 periods, but a fraction does not permit a 21st full monthly payment. Check the discrete table. A logarithmic approximation is useful only with existence conditions and payment timing; the table is clearer when the last actually funded month matters.
Preserve a number or purchasing power
Nominal preservation means leaving the same monetary sum. Real preservation means retaining the ability to buy a comparable basket of goods. The Bank of Russia explains inflation through changes in the general price level, while a personal goal may become more expensive differently.[2](#source-save-inflation) “Spend all interest while principal stays unchanged” therefore does not ensure real preservation.
Educational annual example: 1,000,000 roubles, a net assumed annual increase of 8% and a 6% increase in the comparable basket. After accrual, balance is 1,080,000. To preserve starting purchasing power at year-end, leave 1,060,000, so a one-time payment could be 20,000 in this strictly defined model. This is not a universal safe rule; withdrawal sequence or unknown inflation changes the task.
Errors that hide depletion
Do not confuse a fixed payment with fixed income. Do not subtract annual inflation from a monthly rate. Do not apply average market return as a fixed credit to every balance: with variable results, return order and withdrawals matter. Do not extend the calculation for life without checking the horizon. A useful report shows starting capital, total withdrawals, accruals and ending balance separately, alongside the price basis for real assessment.
Check monetary preservation
At the end of each chosen interval, write the identity: starting capital plus accruals minus withdrawals equals ending balance. It does not replace real-preservation analysis, but exposes omitted movements. A transfer between the owner’s accounts is not consumption; a purchase outside the observation boundary is a withdrawal. For uncertain income, retain several paths rather than only the average. The same average rate does not ensure the same payment horizon. See [real return](/guides/inflation-real-return/) and [savings risks](/guides/savings-risk/) for context.