Your savings rate decides both how fast the pot grows and how big it has to be, which is why it matters more than your income.
The number of years until your investments can pay for your spending depends almost entirely on the share of your take-home pay you save. Starting from nothing, at an illustrative 5 per cent real return and the 4 per cent rule, saving 20 per cent takes 36.7 years, saving 30 per cent takes 28.0, and saving 50 per cent takes 16.6. The figures are the same on any income, because the target is set by what you spend.
Worked in full in Stock Market Investing for Beginners by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Every pound or dollar you do not spend does two jobs. It goes into the portfolio, and it lowers the spending the portfolio will one day have to replace. Under the 4 per cent rule, the target is 25 times yearly spending, as worked in how much you need to retire with the 4% rule. So a higher savings rate fills the pot faster and shrinks it at the same time.
| Input | Value |
|---|---|
| Take-home pay, a year | 50,000 |
| Savings rate, base case | 20% |
| Real return, after inflation and costs | 5.0% |
| Withdrawal rate in retirement | 4.0% |
| Target as a multiple of yearly spending | 25 |
| Savings at the start | 0 |
Everything is in real terms, so the target is in today's money and the return is what is left after inflation. How to turn a nominal return into a real one is worked in how to calculate real return after inflation. Saving is assumed to happen once a year, at the year end, which keeps the formula short.
Step 1, the target. Saving 20 per cent of 50,000 is 10,000 a year, so spending is 40,000. The target is 25 × 40,000 = 1,000,000.
Step 2, the years. The future value of a yearly saving S at return r after n years is S × ((1 + r)n − 1) ÷ r. Set it equal to the target and solve for n:
n = ln(1 + target × r ÷ S) ÷ ln(1 + r)
1,000,000 × 0.05 ÷ 10,000 = 5.0000; ln(6.0000) = 1.7918; ln(1.05) = 0.04879
n = 1.7918 ÷ 0.04879 = 36.7 years
Excel: =NPER(5%, -10000, 0, 1000000)
Step 3, why income drops out. Write S as s × income and the target as 25 × (1 − s) × income. The income cancels, leaving 25 × (1 − s) × r ÷ s inside the logarithm. At 100,000 of take-home pay, saving 20 per cent takes 36.7 years, exactly as at 50,000.
Raise the savings rate to 30 per cent. Saving becomes 15,000, spending 35,000, and the target 875,000. The same formula gives 28.0 years, 8.7 years sooner. Split the gain into its two sources by holding the target at 1,000,000 with the higher saving:
| Case | Yearly saving | Target | Years |
|---|---|---|---|
| 20% saved | 10,000 | 1,000,000 | 36.7 |
| 30% saved, target unchanged | 15,000 | 1,000,000 | 30.05 |
| 30% saved, spending lower | 15,000 | 875,000 | 28.0 |
Saving more is worth 6.7 years; needing less is worth another 2.1. A plan that counts only the first effect understates what a cut in spending buys.
| Savings rate | Target on 50,000 | 3% real | 5% real | 7% real |
|---|---|---|---|---|
| 10% | 1,125,000 | 69.3 | 51.4 | 41.7 |
| 15% | 1,062,500 | 56.1 | 42.8 | 35.3 |
| 20% | 1,000,000 | 46.9 | 36.7 | 30.7 |
| 25% | 937,500 | 39.9 | 31.9 | 27.1 |
| 30% | 875,000 | 34.2 | 28.0 | 24.0 |
| 40% | 750,000 | 25.5 | 21.6 | 19.0 |
| 50% | 625,000 | 18.9 | 16.6 | 15.0 |
| 60% | 500,000 | 13.7 | 12.4 | 11.4 |
| 70% | 375,000 | 9.4 | 8.8 | 8.3 |
Read across a row and the return matters a great deal at low savings rates: at 10 per cent saved, the gap between 3 and 7 per cent real is 27.6 years. Read down a column and the savings rate matters more than any plausible change in return. At 50 per cent saved, the return moves the answer by under four years. The higher your savings rate, the less your plan depends on what markets do.
At a zero real return the formula collapses to 25 × (1 − s) ÷ s: 100.0 years at 20 per cent saved, 25.0 at 50 per cent. Compounding is what turns the first figure into 36.7.
n = ln(1 + target × r ÷ saving) ÷ ln(1 + r), with the target at 25 times spending. At 5 per cent real: 36.7 years at a 20 per cent savings rate, 28.0 at 30, 16.6 at 50, on any income. Money already invested shortens it: 100,000 at the start brings the 20 per cent case down to 28.4 years. Try your own spending, fees and return in the free workbook for this book. All figures are illustrative and none is a forecast or advice.
About 16.6 years at an illustrative 5 per cent real return, starting from nothing and using the 4 per cent rule. Spending half your pay means the pot must be 25 times that half, and saving the other half fills it quickly. At a 3 per cent real return it takes 18.9 years, at 7 per cent 15.0.
Not on its own. The years depend only on the share saved, because the target is set by spending. On 50,000 or 100,000 of take-home pay, saving 20 per cent at 5 per cent real takes 36.7 years either way. A higher income helps only if it raises the savings rate rather than the spending.
Existing savings shorten the time. With 100,000 already invested, saving 20 per cent of 50,000 at 5 per cent real reaches the 1,000,000 target in 28.4 years instead of 36.7. The formula becomes n = ln((target x r + saving) / (savings so far x r + saving)) / ln(1 + r).
This article is one calculation from Stock Market Investing for Beginners. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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