What must be saved to get there
Work backwards from the income wanted to the pot needed, forwards from the salary to the pot built, and the required savings rate is where the two meet.
- Price the pot a retirement income needs
- Compute the pot a savings rate builds, and the gap
- Solve for the savings rate that closes the gap
- Say why retiring later moves the rate more than anything else
The intuition
A client earns $90,000 and wants 70% of that, $63,000 a year, for thirty years of retirement, from savings alone. At a 3% real return that income costs about $1,235,000 on the day they stop working: not thirty times the income, but under twenty, because the pot keeps earning while it is spent. That is the pot needed.
Now run forwards. Saving 10% of salary for thirty years at 3% real builds about $428,000, less than half the need. The required savings rate is the share of salary at which the two meet: here nearly 29%, which is why the conversation usually turns to the retirement date. Work five more years and the rate drops to about 20%: five more years of saving and five fewer years of spending, at the same time. No plausible change in returns moves the rate that far.
Income needed = replacement ratio × salary. Pot needed = income × (1 − (1 + r)^−R) ÷ r. Pot built = PV (1 + r)ⁿ + s × salary × ((1 + r)ⁿ − 1) ÷ r. Required rate s = (pot needed − PV grown) ÷ (salary × annuity growth factor).
Why it works
- The conventions here: everything real, with a flat real salary. The client saves a fixed share of salary at the end of each working year at a constant real return, and draws a replacement income for a stated number of retirement years, at year end, running the pot to zero. No taxes, fees, pension or other income. The work-longer comparison adds five working years and removes five retirement years.
- The pot needed is a present value. Income × the annuity factor for the retirement years. Under twenty times the income at a 3% real return, against the 25 times a 4% rule asks for, because this pot is spent to zero with no buffer.
- The pot built is a future value, the same formula as chapter 1 in real terms: the existing balance grown, plus savings through the annuity growth factor.
- The required rate is where they meet: what remains of the need after the existing balance has grown, spread over salary times the growth factor.
- Retiring later works twice. A smaller pot is needed, because it must last fewer years, and there is longer to build it. Together they move the rate far more than a point of return.
- A higher assumed return is not a fix. It changes the spreadsheet, not the markets, and adds the risk that the plan fails exactly when the client can least afford it. Retiring later or spending less changes the actual cash flows.
| Income needed: 70% × $90,000 | $63,000 a year |
| Annuity factor, 30 years at 3%: (1 − 1.03⁻³⁰) ÷ 3% | 19.600 |
| Pot needed: $63,000 × 19.600 | $1,234,828, 19.6 times the income |
| Growth factor for level saving, 30 years: (1.03³⁰ − 1) ÷ 3% | 47.575 |
| Pot built at 10%: $9,000 × 47.575 | $428,179, so $806,649 short |
| Required rate: 1,234,828 ÷ (90,000 × 47.575) | 28.84% |
| Working 5 more years: need $1,097,028, factor 60.462 | 20.16% |
Five more years took nearly nine points off the savings rate. A point more return would take about three.
The formulas
What the client wants each year, in today's dollars.
The present value of that income for R years.
The existing balance grown, plus savings through the growth factor.
Where built meets needed, solved for the rate.
Worked example
Income needed first, then the annuity factor for the retirement years, then multiply. The follow-up compares the multiple with a 4% rule.
See it move
Same client. Change the salary, the real return, the working and retirement years, the replacement ratio and the share of salary saved today.
- Raise the share of salary saved. The pot built rises; the pot needed does not move. The crossing on the first curve is the required rate.
- Raise the replacement ratio. The pot needed rises; the pot built does not move.
- Add retirement years. The pot needed rises; add working years and the pot built rises instead. Retiring later does both at once.
- Raise the real return. The pot needed falls and the pot built rises; both help, but watch how much less it moves the crossing than five working years do.
Run it backwards
The pot needed and the working years are known. Take off what the existing balance will grow to, and divide the rest by salary times the growth factor.
The existing balance does its part on its own. What is left to build, divided by the growth factor, is the annual saving in dollars; over the salary it is the rate.
If that rate is one the client cannot afford, the levers are the retirement date, the replacement ratio and the salary, in roughly that order of power.
Traps
Say it in the interview
“What savings rate does this client need, and what if they cannot afford it?”
Check yourself
4 fresh questions, with new numbers. Answer each one correctly to finish the chapter. Get one wrong and you will see the full working, then you can try it again with new numbers.
Answers within 1% are marked right. Type the number; $, %, x and M are fine. First tries count toward Learned: the topic is Learned once every chapter is done and 75% of first tries were right.
- Pot needed = income × PV annuity factor over the retirement years.
- Pot built = PV grown + savings × growth factor over the working years.
- Required rate = (need − PV grown) ÷ (salary × growth factor).
- Retiring later works twice: less needed, longer to build it.