Retirement Planning
How a retirement plan is built and tested: what saving compounds to, what those dollars will buy, what a pot can pay out, the savings rate that closes the gap, and when to claim the pension.
Every retirement plan answers the same five questions, and interviewers ask them in the same order. How much will the saving build? What will those dollars buy once prices have risen? How much can the pot pay out, and for how long? What share of salary closes the gap between the two? And when should the client turn on the pension? This lesson takes them one at a time, with the arithmetic that answers each.
Two tools do most of the work. The annuity factor turns a stream of level payments into a lump and back again: ((1 + r)ⁿ − 1) ÷ r growing savings forward, (1 − (1 + r)^−N) ÷ r pricing withdrawals backward. And the real return, (1 + nominal) ÷ (1 + inflation) − 1, keeps the whole plan in today's dollars so the client can recognize the numbers.
- Build. A balance grown plus contributions through the annuity factor; the price of starting late.
- Buy. Real against nominal; the future cost of today's spending; tax on the inflation part.
- Pay out. Withdrawal rates, how long a pot lasts, the most it can pay, and sequence risk.
- Close the gap. The pot needed against the pot built; the required savings rate; retiring later.
- Claim. Check sizes, cumulative totals, the break-even age, and the survivor benefit.
Keep the plan in real terms and let the annuity factor do the adding up. Anything paid in compounds through the growth factor; anything paid out is priced with the present-value factor; and a steady-return answer is an upper bound, because real returns arrive in a random order. The buffers and spending rules that manage that sequence risk are named in the pay-out chapter.
A plan, from the first contribution to the pension
Each step points to the chapter that practices it.
Chapters
What saving builds
11 minTwo engines run at once: the balance already there, compounding, and a stream of new contributions, each compounding for a shorter time than the one before.
- Compute the future value of a balance plus level contributions
- Split an ending balance into what was paid in and what compounding added
- Find the contribution a target needs
- Put a price on starting late
What those dollars will buy
10 minA retirement plan is a promise about purchasing power, not dollars. Inflation converts one into the other, and tax on the nominal return makes it worse.
- Compute an exact real return, and say how far the shortcut is off
- Inflate today's spending to the year it is needed
- Find the nominal return a real target needs
- Compute an after-tax real return and say why it can be negative
What a pot can pay out
12 minA retirement portfolio is a race between what it earns and what the client takes out. Below the real return the money lasts forever; above it, the decline accelerates.
- Compute a withdrawal rate and the spending a rule allows
- Work out how long a pot lasts at a steady real return
- Size the portfolio a spending goal needs under a rule
- Find the most a pot can pay for exactly N years, and say why the 4% rule is lower
What must be saved to get there
12 minWork 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
When to claim the pension
11 minClaim early and get more years of a smaller check; wait and get fewer years of a bigger one. The totals cross at an age, and the decision is a bet on living past it.
- Size the monthly benefit at an early and a late claiming age
- Compare cumulative totals by a given age
- Find the break-even age
- Say who should wait, and why the survivor benefit matters