United States
Hong KongTime value of money: the skill that pays across the whole paper
Five variables - number of periods, rate, present value, payment and future value. Given any four you solve for the fifth. The recurring errors are sign convention, periods per year, and confusing an annuity due with an ordinary annuity.
One skill, used in retirement, education, investment, insurance and estate questions. Nothing else on the exam has that reach.
The five variables
- N - the number of periods.
- I/Y - the interest or discount rate per period.
- PV - present value.
- PMT - the payment per period.
- FV - future value.
Four known, solve for the fifth. That is the whole mechanism, and the difficulty is entirely in the setup.
The three setup errors
Sign convention. Money out is negative, money in is positive. Enter a contribution as positive and a withdrawal as positive and the calculator returns something meaningless.
Periods per year. Monthly payments mean N in months and I/Y divided by twelve. Half of all wrong answers here are annual rates applied to monthly periods.
Annuity due versus ordinary annuity. Payments at the beginning of the period rather than the end. Rent, insurance premiums and lease payments are typically due; loan payments and most savings contributions are ordinary.
A calculator left in BEGIN mode from a previous question quietly changes every subsequent answer. Getting into the habit of resetting it is worth more than it sounds, and it is the single most common self-inflicted error on this material.
What the exam actually asks
| Question type | Setup |
|---|---|
| How much will this grow to | PV, I/Y, N, solve FV |
| What is a future sum worth today | FV, I/Y, N, solve PV |
| How much must I save each month | FV, I/Y, N, solve PMT |
| How long will this last | PV, PMT, I/Y, solve N |
| What return is implied | PV, FV, N, solve I/Y |
| Uneven cash flows | Cash flow register, then NPV or IRR |
Inflation-adjusted returns
The real rate is not the nominal rate minus inflation, though that approximation is close at low rates. The exact version divides one plus the nominal by one plus inflation, less one.
Retirement questions frequently want the inflation-adjusted rate, and using the approximation on a question expecting the exact form produces an answer close enough to be a plausible distractor.
How to practice
On the calculator you will take, not on a spreadsheet. Keystrokes are motor memory and they need to be automatic under time pressure.
Twenty problems, spread over several sessions, is usually enough to get there. It is the cheapest reliable improvement available on this exam.
Every dollar limit here is indexed annually and several were changed by recent legislation. Confirm the current figure against the IRS or the relevant authority before relying on it, and expect the exam to test the rule rather than the number.
Common questions
What are the five time value of money variables?
Number of periods, interest rate per period, present value, payment and future value. Given any four you solve for the fifth.
What is the most common TVM error?
Mismatched periods - using an annual rate with monthly periods. Sign convention and leaving the calculator in BEGIN mode are close behind.
What is the difference between an annuity due and an ordinary annuity?
Payment timing. An annuity due pays at the beginning of each period - rent, insurance premiums, leases. An ordinary annuity pays at the end - loan payments and most savings contributions.
How do you calculate a real return?
Divide one plus the nominal rate by one plus inflation, then subtract one. Subtracting inflation from the nominal rate is an approximation that produces a plausible wrong answer.
How much practice does this need?
About twenty problems spread over several sessions, on the calculator you will actually take. Keystrokes are motor memory and need to be automatic under time pressure.