Time value of money calculator (N, I/Y, PV, PMT, FV)

Fill in four of the five boxes and leave one empty. It solves for the empty one the way the exam calculator's TVM keys do, so you can check your keystrokes and your answers.

How it works

Every time value problem is one equation. With a periodic rate r (the annual rate ÷ periods per year), N periods, and b = 1 for payments at the start of each period or 0 at the end:

PV + PMT × (1 + r×b) × [1 − (1 + r)^−N] ÷ r + FV × (1 + r)^−N = 0

Four known values fix the fifth. A lump sum has PMT = 0; a loan with no balance at the end has FV = 0; an annuity has both PV (or FV) and PMT.

A worked example

You put 5,000 into an account paying 6% a year compounded monthly and leave it for 10 years. Enter N = 120 (10 years × 12), I/Y = 6, PV = −5,000, PMT = 0, periods per year = 12, and solve for FV: 9,096.98. The monthly rate is 6% ÷ 12 = 0.5%, applied 120 times.

Common mistakes on the exam

Set the periods per year to match the compounding, and enter N in periods, not years: ten years of monthly payments is N = 120.
Mind the signs. Money you pay out and money you receive have opposite signs; two inflows with nothing out has no answer.
Annuity due (payments at the start of each period) is worth one period of interest more than an ordinary annuity. Switch the mode when a payment is made today.
Reset the calculator between problems: a leftover payment or a begin setting is the most common source of a wrong answer.

The exam allows only certain calculator models, and the rules change: check CFA Institute's current calculator policy before you rely on any keystroke here.

Where this is taught

Restate a yield at a different compounding frequency CFA Level I · Fixed Income
Work out what an annuity and a perpetuity are worth today CFA Level I · Quantitative Methods
Explain continuous compounding and the lognormal distribution CFA Level I · Quantitative Methods
Work out a project's internal rate of return and net present value, and explain each CFA Level I · Corporate Issuers

Read the guide

Time value of money explained: present value, future value and annuities

Practise what you read

Today's practice question One question, with every wrong option explained.
Free Level I diagnostic test Twelve questions that show which topics to start with.
Free finance calculators Check your arithmetic on the exam's core formulas.

Questions people ask

How do I solve for the interest rate?

Fill in N, PV, PMT and FV and leave I/Y empty. The rate is found numerically, because no formula isolates it. With PV = −1,000, FV = 1,500 and N = 5 it returns about 8.45% a year.

What is the difference between an ordinary annuity and an annuity due?

An ordinary annuity pays at the end of each period; an annuity due pays at the start. Each payment of an annuity due is one period closer, so its value is higher by a factor of (1 + r).

Why does the answer have the opposite sign to my input?

The equation balances cash flows: what you pay in against what you get out. Solving for FV from a negative PV returns a positive FV, which is the money you will receive.

Practise this until the arithmetic is automatic: questions on every topic, with the reason each wrong option is wrong.

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