F. Financial Literacy · Financial Decisions: Interest, Borrowing, Appreciation, Depreciation and Budgets

Appreciation and Depreciation in Real Life

F1.2 F1.1About 65 minutes

Learning goals

I can explain appreciation and depreciation and give real examples of each.
I can identify financial situations that involve appreciation or depreciation, and explain why the value changes.
I can calculate the amount and the percent of appreciation or depreciation.
I can read a graph of value over time to answer questions, including when a loan balance is more than an item's value.

Words to know

appreciation
An increase in the value of something over time.

depreciation
A decrease in the value of something over time.

market value
What something could be sold for today.

percent appreciation or depreciation
(new value − original value) ÷ original value × 100%. A negative result means depreciation.

asset
Something you own that has value, such as a car, a home, savings or shares.

negative equity
When you owe more on a loan than the item is worth. Also called being "underwater" on a loan.

Hook: the car that loses money in the driveway

A family buys a brand-new $30 000 car. One year later they decide to sell it, but buyers offer only about $25 500. The car still runs perfectly. Where did $4 500 go?

The car depreciated: its value went down over time. Meanwhile, a neighbour's building lot that cost $80 000 might be worth more than that a year later: it appreciated.

Expectation F1.2 asks you to identify financial situations that involve appreciation and depreciation, and to use graphs to answer questions about them. All values here are examples.

What changes the value of things?

Depreciation often happens because of:

wear and tear (kilometres on a car, scratches on a phone),
age and new models (a newer phone comes out every year),
less demand (fewer people want the old version).

Appreciation can happen because of:

rarity (only a few of a hockey card exist),
growing demand (more people want to live in a town),
location (land near a new transit line or a lake),
inflation (prices in general are rising, Lesson 1).

Appreciation is never guaranteed. Home prices, collectibles and shares can also fall. For example, after early 2022, when interest rates rose quickly, home prices in many Ontario communities dropped for a while.

Common examples. Many things we buy depreciate. Some things may appreciate, but they can also lose value, so the right column says "may".

Calculating appreciation and depreciation

Amount of change = new value − original value
Percent change = (new value − original value) ÷ original value × 100%

If the answer is positive, the item appreciated. If it is negative, the item depreciated. People usually say "it depreciated by 60%" rather than "−60%".

Worked example

Example 1: A phone depreciates

A phone cost $1 000 new. Two years later it sells for $400. Find the amount and percent of depreciation.

Amount: 400 − 1000 = −600, so it lost $600.
Percent: −600 ÷ 1000 × 100% = −60%.

The phone depreciated by $600, or 60%, in two years.

Worked example

Example 2: A hockey card appreciates

Dev bought a rookie hockey card for $40. Three years later, a similar card sold online for $65. Find the percent appreciation.

Amount: 65 − 40 = $25.
Percent: 25 ÷ 40 × 100% = 62.5%.
Context: the card is worth $65 only if someone actually buys it at that price. Collectibles can also drop if a player's career slows down or the trend fades.

The card appreciated by about 62.5%, but this value is not guaranteed.

The building lot's graph rises (appreciation) and the car's graph falls (depreciation). The car loses the most value in its first year.

Worked example

Example 3: Answer questions from the graph

Use the graph of the car and the building lot.

(a) About how much is the car worth after 2 years? (b) Which item changes by more dollars in the first year? (c) After 5 years, about how much more is the lot worth than when it was bought?

(a) Find 2 on the horizontal axis, go up to the car's (dashed) line, then across: a little more than $20 000. The exact value is $21 675.
(b) The car drops from $30 000 to $25 500, a change of $4 500. The lot rises from $80 000 to $83 200, a change of $3 200. The car changes by more.
(c) After 5 years the lot is just under $100 000 (exact: about $97 332). 97 332 − 80 000 ≈ $17 332.

(a) about $21 700; (b) the car ($4 500 compared with $3 200); (c) about $17 300 more.

A financial situation: depreciation plus a loan

Depreciation becomes a real problem when you borrow to buy something that loses value. Suppose the family bought the $30 000 car with $0 down and an 84-month loan at 7% (payment $452.78). The car loses value faster than the loan is paid down at first.

For about the first three years the loan balance (solid line) is above the car's value (dashed line). If the car is written off or sold then, the family still owes money on a car they no longer have.

Why this matters

Owing more than something is worth is called negative equity. A down payment (Lesson 5), a shorter loan (Lesson 4), or buying a slightly used car whose biggest drop in value has already happened can all help you avoid it.

Hands-on activity

Value detective

You need: a grown-up, an online marketplace or classified ads (with a grown-up's help), a notebook.

Choose three items your family owns or wants: for example a bike, a phone, a game console, a hockey card or a used car.
Find (or ask about) the price when new and today's typical selling price for a used one of the same model.
Calculate the amount and the percent change for each.
Sort them: appreciated or depreciated? Write one reason for each.
Ask a grown-up: "Have you ever sold something for more or less than you paid? What happened?"

Model answer: bike bought for $600, similar used bikes sell for about $350: depreciation of $250, or about 41.7%, because of wear and newer models.

Just for fun

A new car starts depreciating the moment it leaves the lot. Good news: the jokes in this unit started with a value of zero, so they can only appreciate.

Your turn

A laptop cost $1 500 and is worth $600 three years later. Find the amount and percent of depreciation.

A painting was bought for $250 and sold for $400. Find the percent appreciation.

Sort into "usually depreciates" and "may appreciate": a snowmobile, a house in a growing town, a smartphone, a rare coin, a winter jacket.

Use the graph: about how much is the new car worth after 1 year? By what percent did it depreciate?

Use the loan-balance graph data: after 1 year the family owes $26 557.58 and the car is worth $25 500. What is the negative equity?

Give one reason a 2- or 3-year-old used car can be a better buy than a new one.

More practice: warm-up

What does appreciation mean?

An item drops from $200 to $150. What is the amount of depreciation?

What percent is that depreciation?

A value-over-time graph goes down from left to right. Is this appreciation or depreciation?

Name one thing that usually depreciates.

More practice: on your own

A hockey card bought for $12 is worth $3 a few years later. Find the percent change. What does this show about collectibles?

A home bought for $420 000 sells for $504 000. Find the percent appreciation. If selling costs are 5% of the sale price, what is the gain after costs?

A $14 000 snowmobile loses 40% of its value in 3 years. What is it worth?

Use the building lot data ($80 000, then about $97 332 after 5 years). Find the percent appreciation over the 5 years.

A 4-year-old TV cost $1 200 and its depreciated value is now $300. A new similar TV costs $900. If it is stolen, how much would a "depreciated value" insurance policy pay compared with a "replacement cost" policy?

Challenge

Use the data under the loan graph (balances: year 3 $18 908.18, year 4 $14 663.95; values: year 3 about $18 424, year 4 about $15 660). In which year does the car's value become greater than the loan balance?

An item depreciates 20% one year and then appreciates 20% the next. Is it back to its original value? Explain with an example.

Car A is new for $30 000. Car B is the same model, 3 years old, for $18 500. Both lose 15% of their value each year. How much value does each lose in the next 3 years?

Check your understanding

Quiz

Which item is most likely to depreciate?

A bike cost $800 and is worth $500 now. What is the percent depreciation?

A value-over-time graph rises from left to right. What does it show?

Which statement about appreciation is true?

You owe $12 000 on a car worth $9 000. What is this called?

A card bought for $40 sells for $65. What is the percent appreciation?

For parents and teachers

Big idea: F1.2 asks students to identify financial situations that involve appreciation and depreciation and use associated graphs to answer questions. This first lesson builds the ideas and the percent-change math. Lessons 9 and 10 look at the two main shapes of these graphs: straight lines and curves. The car-loan graph connects back to borrowing (F1.3) and shows how the two ideas interact.

Common difficulties:

Dividing by the new value instead of the original value when finding percent change.
Assuming homes or collectibles always go up. Encourage "may appreciate".
Reading graphs too precisely. Values read from a graph are estimates; say "about".

How to help: Look up the used price of something your family owns (a bike, a phone, a car) and compare it with what you paid. Talk about why it changed. If your teen collects cards or other items, discuss how their value can go up or down.