How Long Savings Last
What remains keeps earning interest, so the money lasts longer than the lump sum divided by the withdrawal. Once the withdrawal exceeds the interest, though, the principal starts falling and the interest falls with it, so the decline accelerates.
Your numbers
Years
23.13yr
Months
277.6mo
Total repaid
416,407,952
Formula
Years = −ln(1 − Principal × i ÷ Amount) ÷ ln(1 + i) ÷ 12
Rising prices shrink what the same amount buys. To read the answer in today’s money, enter the return minus inflation.
What to enter
| Input | Default | Accepted range |
|---|---|---|
| PrincipalThe money you put in — the base that earns interest. | 300,000,000 | 0 and up |
| Annual rate (%)Interest quoted per year; the monthly rate is this over 12. | 3 | 0 and up |
| AmountThe amount the calculation starts from — settle whether tax is inside it. | 1,500,000 | 0 and up |
Step by step
Quick reference table
Results when only Principal changes and everything else stays put.
| Principal | Years (yr) | Months (mo) | Total repaid |
|---|---|---|---|
| 150,000,000 | 9.6 | 115.2 | 172,824,915 |
| 225,000,000 | 15.69 | 188.2 | 282,354,534 |
| 300,000,000 | 23.13 | 277.6 | 416,407,952 |
| 450,000,000 | 46.27 | 555.2 | 832,815,905 |
| 600,000,000 | 0 | 0 | 0 |
What each result means
| Result | At default values |
|---|---|
| Years (yr)How many years the money stays put; compounding bites harder as this grows. | 23.13 |
| Months (mo)The period counted in months; a yearly rate gets divided by twelve. | 277.6 |
| Total repaidEverything handed over by the last payment — principal plus interest. | 416,407,952 |
Common mistakes
Rising prices shrink what the same amount buys. To read the answer in today’s money, enter the return minus inflation.
Glossary
- Principal
- The money you put in — the base that earns interest.
- Annual rate
- Interest quoted per year; the monthly rate is this over 12.
- Amount
- The amount the calculation starts from — settle whether tax is inside it.
- Years
- How many years the money stays put; compounding bites harder as this grows.
- Months
- The period counted in months; a yearly rate gets divided by twelve.
- Total repaid
- Everything handed over by the last payment — principal plus interest.
Frequently asked questions
Q. How is How Long Savings Last calculated?
Years = −ln(1 − Principal × i ÷ Amount) ÷ ln(1 + i) ÷ 12 — What remains keeps earning interest, so the money lasts longer than the lump sum divided by the withdrawal. Once the withdrawal exceeds the interest, though, the principal starts falling and the interest falls with it, so the decline accelerates.
Q. Can you walk through an example?
With Principal 300,000,000, Annual rate 3%, Amount 1,500,000, the answer is Years 23.13yr.
Q. What do I need to enter?
Enter Principal, Annual rate, Amount. The result recalculates as you type, and an empty box counts as zero.
Q. How much does the answer move if I change a number?
Changing only Principal moves the answer to Principal 150,000,000 → Years (yr) 9.6 and Principal 600,000,000 → Years (yr) 0. The table below lays out five steps.
Q. How are the numbers rounded?
Money is shown to the nearest whole unit, percentages to one decimal place and everything else to two. What you see is rounded; the calculation itself carries the unrounded value forward.
Q. Anything to watch out for?
Rising prices shrink what the same amount buys. To read the answer in today’s money, enter the return minus inflation.
Related calculators
Tax rates and interest conventions differ by country and product — check your contract for real transactions.