Every concept, endless questions
Each concept is a small financial model. Read how it works, then draw a real interview question from it: forwards, backwards or what-if, with fresh numbers and a worked solution every time.
Forward runs a concept the usual way. Inverse runs it backwards, which is what separates understanding from memorizing.
Retirement Planning
5 conceptsFuture value with regular contributions
Retirement saving is two engines running at once: the balance you already have, compounding, and a stream of new contributions, each of which compounds for a shorter time than the one before. Early on the contributions do almost all the work; after a couple of decades the growth on the balance overtakes them, and by the end most of the money in the account was never contributed at all. That is why the cost of starting late is so much bigger than the missing contributions — the dollars skipped were the ones that would have compounded longest.
Safe withdrawal rate
A retirement portfolio is a race between what it earns and what the client takes out. If the withdrawal is no bigger than the real return, the money never runs out; every dollar above that is eaten out of capital, and the capital then earns less next year, so the decline accelerates. The famous 4% rule is a rough answer to "how much can I take, rising with inflation, and still survive a bad sequence of markets over thirty years?" Constant-return arithmetic understates the danger, because it never has a crash in year two — but it is the right place to start, and the right way to see how sensitive the plan is to the return.
Required savings rate
Every retirement plan reduces to one number the client controls: the share of salary they save. Work backwards from the income they want in retirement, the years it must last and the return they can expect, and the plan tells you the pot they need on the day they stop working. Work forwards from their salary, years of work and the same return, and it tells you what each point of savings builds. The required rate is where the two meet. Its most useful property is how violently it responds to the retirement date: working a few years longer both adds contributions and removes withdrawals, so it moves the rate far more than any plausible change in returns.
Claiming-age tradeoff
Claiming a public pension early buys more years of checks at a permanently smaller size; waiting buys a bigger check for fewer years. The early claimer races ahead, and the late claimer catches up a little every month, so there is an age at which their cumulative totals cross. Live past it and waiting won. Framed that way, claiming is a bet on your own longevity — and, because the delayed benefit is inflation-linked and lasts for life, it is also the cheapest longevity insurance most retirees can buy. For a married higher earner it doubles as a larger survivor benefit.
Real versus nominal returns
A retirement plan is a promise about what money will buy, not how many dollars there will be. Inflation quietly converts one into the other: at 3% a year, a dollar buys about half as much in twenty-four years. The return that matters is therefore the real return — what is left after prices rise — and for anything held in a taxable account, what is left after the tax on the nominal return as well. That second step is the one clients miss: tax is charged on the part of the return that merely kept up with inflation, so a bond yielding comfortably above inflation can still lose purchasing power once the tax bill arrives.