Simple Return - a beginner's guide

Domain: D00 — Financial Mathematics, Statistics, and Data Foundations
Family: D00-F02 — Financial Arithmetic, Time Value, and Returns
Audience: a curious beginner who may not have studied finance or programming
Delivery: plain-language lesson, hand-worked arithmetic, and a small interactive lab

The one-sentence idea

Measure the change from a starting investment to an ending value, including cash received along the way.

Why this matters in money

People often say an asset 'returned 10%' without saying whether dividends, coupons, fees, or the starting price were included. A simple return makes the numerator and denominator visible.

What you will be able to do

calculate a holding-period return from start, end, and cash received
separate price return from total return
state the period and exclusions beside the percentage

What you need first

D00-F01 ratios and percentage change
D00-F02-A03 date awareness

You do not need to program for this lesson. We use ordinary words and small numbers first. Later domains may show implementation details after the idea is comfortable.

Words to know

Term	In simple words
Starting value	The value at the beginning of the measured period.
Ending value	The value at the end.
Cash received	Dividends, coupons, or other cash included in the return definition.
Total return	Price change plus included cash, divided by the starting value.

Scope and simple boundary

We use one starting value, one ending value, and cash received during the period. Fees, taxes, reinvestment timing, leverage, and currency conversion are excluded unless explicitly added.

Definition contract

Decision	Our simple choice	What we do not claim	Check
Denominator	Use the starting value as the base.	Do not divide by the ending value for this definition.	The example writes start in the denominator.
Cash	Include cash only when the return is labelled total return.	Do not mix price return and total return labels.	Both values are shown side by side.
Period	Name the measured dates.	A percentage without a period cannot be compared safely.	The example says one holding period.

Input contract

Name	Kind	Unit	Empty?	Meaning
start	money	SAR	No	Value at the beginning.
end	money	SAR	No	Value at the end.
cash	money	SAR	No	Cash received during the period.

All values in one example must use the same time period, currency, and scale unless the lesson explicitly shows a conversion. A missing or impossible input is a question to resolve, not a number to guess.

Output contract

Output	Kind	Unit	Meaning	Safety rule
price_return	percentage	%	(End - Start) / Start.	Start must be non-zero.
total_return	percentage	%	(End + cash - Start) / Start.	Cash definition must be stated.

The rule in everyday language

total return = (ending value + cash received - starting value) / starting value

Think of the rule as a sentence. Say what each number means before you put it into the sentence.

Symbol table

Name	Meaning	Unit
S	starting value	SAR
E	ending value	SAR
C	included cash received	SAR
R	return	decimal or %

Four small steps

Name the start and end dates.
Subtract the starting value from the ending value.
Add included cash if calculating total return.
Divide by the starting value and label the period and costs that were left out.

Worked example (synthetic teaching numbers)

Synthetic example: buy at SAR 100, finish at SAR 108, and receive SAR 2 in cash. Price return = (108 - 100)/100 = 8%. Total return = (108 + 2 - 100)/100 = 10% for the stated holding period.

Independent check

The SAR 2 cash is 2% of the SAR 100 starting value. Adding it to the SAR 8 price gain produces SAR 10 of total gain, or 10%.

The numbers above are synthetic and author-derived for learning. They are not an observation about a named company, market, customer, or investment.

Simple playground

Open the small guided lab. Choose a number, press Step, and read the explanation under the result. The lab is designed to show one idea at a time, not to replace the lesson.

Simple Return lesson map

What to notice: the input, the rule, the check, and the safe interpretation are shown in that order. Open the full-size visual.

Where this is useful

describing one investment period
separating price and cash contributions
checking a return statement before annualizing it

What this does not tell you

This is a measurement of the selected holding period, not a forecast. Fees, taxes, reinvestment timing, dividends declared but not received, and currency can change the definition.

This is educational content, not investment, tax, legal, accounting, or regulatory advice. A simple calculation can be correct and still be the wrong calculation for a real decision.

Historical-example decision

Not useful for this lesson. A named company would add a story but would not teach the primitive more clearly than the small synthetic numbers above. A real case would also need a verified entity, period, unit, and publication right. The lesson therefore keeps its arithmetic transparent and synthetic.

Related lessons

Evidence boundary

The plain-language definitions and measurement cautions are supported by INVESTOR_RETURN, CFA_QM. The formula wording, examples, and lab behavior are author-derived teaching choices. See the claim ledger and references for the boundary.

Optional verification implementation

You do not need code to learn this lesson. The package now includes matching Python and TypeScript verification façades, a shared worked-example fixture, and parity tests. They reproduce the lesson’s frozen rule and remain optional for nontechnical learners.

Enhancement studio: draw, compare, explain

This additive studio does not replace the beginner lesson above. It gives you two more drawings, a decision comparison, and short practice prompts so you can explain the idea without copying a formula or writing code.

Drawing 1 — name, apply, check

Three-part concept anatomy for Simple Return

Read left to right: name what the data means, apply the narrow lesson rule, then use an independent check. Open the full-size concept anatomy.

Choose the right idea

Decision	This lesson	Closest next or comparison	Why the difference matters
Main question	Measure the change from a starting investment to an ending value, including cash received along the way.	Log Return	Choose the question before choosing the arithmetic.
Safe rule	total return = (ending value + cash received - starting value) / starting value	Uses its own input and boundary contract.	Neighboring lessons can use the same numbers but answer different questions.
Required check	The SAR 2 cash is 2% of the SAR 100 starting value. Adding it to the SAR 8 price gain produces SAR 10 of total gain, or 10%.	Re-check its own unit, time, denominator, or schema.	A correct answer to the wrong question is still wrong.
Stop condition	Do not divide by the ending value for this definition.	Move only when its prerequisites are satisfied.	Unknown meaning is a reason to pause, not to guess.

Drawing 2 — common-mistake clinic

Safe reading compared with a tempting mistake for Simple Return

The left side states the safe interpretation; the right side shows the mistake that often produces a believable but misleading result. Open the full-size mistake comparison.

Explain it back without code

Name it: What does the first input or observation mean?
Answer: Value at the beginning.
Choose it: Which rule belongs to this question?
Answer: total return = (ending value + cash received - starting value) / starting value
Challenge it: What check could make you stop?
Answer: The SAR 2 cash is 2% of the SAR 100 starting value. Adding it to the SAR 8 price gain produces SAR 10 of total gain, or 10%.

If your explanation leaves out the unit, period, denominator, grain, or availability time that the lesson needs, it is not complete yet.

Related concepts and learning handoff

Governed glossary: Starting value, Ending value, Cash received, Total return. Browse the full financial glossary when a term is unfamiliar.
Continue with: Log Return.
Evidence boundary: all displayed numbers remain synthetic teaching data; the drawings do not claim a market observation, forecast, or investment result.

Workflows

Rendered from the canonical Mermaid sources linked by this article.

Simple Return — four-part map

This diagram shows the learner's path from a named input to a safe explanation.

Rendering system map…

Takeaway: the check is not an afterthought. It tells the learner whether the answer belongs to the question that was asked.

ReferencesPrimary sources and evidence notes

Expand the source trail, evidence role, and limitations behind the engineering choices.

Each source has a limited evidence role. The worked values, visuals, and playground controls are synthetic and author-derived.

INVESTOR_RETURN - Annual Return

Organization or authors: U.S. Securities and Exchange Commission
Source type: Official investor education glossary
Publication or effective date: Current web edition
Version: current web edition accessed for this build
URL: https://www.investor.gov/introduction-investing/investing-basics/glossary/annual-return
Accessed: 2026-08-10
Jurisdiction: general educational finance or measurement context
Supports: Why a return describes what an investment gained or lost over a stated period.
Limitations: It does not make a return comparable when periods, fees, taxes, or cash-flow timing differ.

CFA_QM - CFA Institute Quantitative Methods Study Session

Organization or authors: CFA Institute
Source type: Professional finance curriculum
Publication or effective date: 2023 Level I curriculum PDF
Version: current web edition accessed for this build
URL: https://www.cfainstitute.org/sites/default/files/-/media/documents/study-session/2023-l1-topics-combined.pdf
Accessed: 2026-08-10
Jurisdiction: general educational finance or measurement context
Supports: Why periodic rates need a stated period and why compounding is multiplicative rather than a simple sum.
Limitations: Curriculum notation is simplified for teaching and does not replace a product's legal terms.

Author-derived and synthetic boundary

The formulas are standard classroom definitions selected for this family. The examples use small synthetic SAR amounts and percentage rates so a learner can reproduce every step by hand. They do not establish a company fact, market outcome, product quote, or investment result.

Implementation

Full dependency-light reference implementations in both supported languages.

algorithm.ts

import { runTopic as runD00Topic, type D00Input, type D00Output } from "../../../../shared/typescript/d00Engine.ts";

/** Run the canonical D00-F02-A06 calculation. */
export function simpleReturn(input: D00Input): D00Output {
  return runD00Topic("D00-F02-A06", input);
}

Playground

The embedded lab now expands to its full document height, keeping the article as the only scroll surface.

Full-height lablessonOpen full screen