VertexMath · MTH1W · Free worksheet

Financial Literacy Review

Try each problem first. You don’t need to finish everything.

Core path ~55 min Full sheet ~1 h 45 min

Recommended: K1–K5, then one A and one T problem

K = Knowledge & Understanding · A = Application · T = Thinking · Boss = Challenge

vertexmath.ca Hints, answers & more worksheets

Show your work on separate paper. Show your work in the dot-grid space.

Core Skills (K)

Budgets · Appreciation & Depreciation · Simple Interest · Compound Interest · Cost of Credit

K1 Sam's Monthly Budget

Sam's gross pay is $3150 a month. Deductions (income tax, CPP and EI) take $640 a month. The table shows Sam's monthly expenses.

$\text{Expense}$	Rent	Car insurance	Phone plan	Groceries	Hydro	Gas	Entertainment
$\text{Cost (\$)}$	$1100$	$160$	$55$	$420$	$85$	$140$	$150$

a)
State whether each expense is fixed or variable.
b)
Determine Sam's monthly net income and total monthly expenses.
c)
Determine Sam's monthly surplus or deficit, and the total for one year.

Stuck? Peek at a hint

A fixed expense is the same amount every month. Net income is gross pay minus deductions.

K2 Value Over Time

a)
A painting worth $1200 appreciates by 5% each year. Find its value after 3 years.
b)
A laptop bought for $1400 depreciates by 30% each year. Find its value after 2 years.
c)
The graph shows the value $V$ , in dollars, of an e-bike at the start and after 1 and 2 years. It loses the same percent of its value each year. Determine that percent, and the value after 5 years.

Stuck? Peek at a hint

A 30% loss leaves 70% of the value, so multiply by $0.70$ once for each year.

K3 Simple Interest

Use $I=Prt$ .

a)
Find the interest earned on $2500 at 4% per year for 3 years.
b)
$1800 is invested at 3.5% per year for 18 months. Find the total amount at the end.
c)
$600 earns $54 in simple interest over 3 years. Determine the annual interest rate.

Stuck? Peek at a hint

Write the time in years and the rate as a decimal before substituting.

K4 Compound Interest

Use $A=P(1+r)^t$ . Interest is compounded annually.

a)
$2000 is invested at 5% per year for 4 years. Find the amount at the end.
b)
Find the interest earned in (a).
c)
A GIC pays 3% per year. Determine how much must be invested today to have $5000 in 6 years.

Stuck? Peek at a hint

In (c), $5000 is the amount $A$ at the end; substitute it and solve for $P$ .

K5 Cost of Credit

A phone costs $1200, taxes included. Plan 1: $150 down, then $49 a month for 24 months. Plan 2: $0 down, then $54 a month for 24 months.

a)
Find the total amount paid with Plan 1.
b)
Find the cost of credit for Plan 1.
c)
Find the total paid and the cost of credit for Plan 2. Which plan costs less overall?

Stuck? Peek at a hint

Add every payment you make, including the down payment, then subtract the price of the phone.

Real World (A)

Saving Goals · Comparing Assets · Car Loans

A1 Saving for a Laptop

Aisha works part-time in Hamilton. Her net pay is $1240 a month. Her monthly expenses are: phone $50, transit pass $128, family contribution $300, food out $260, clothing $150 and entertainment $180. She wants a laptop with a shelf price of $1500 in 6 months.

a)
Find Aisha's monthly surplus. How much must she save each month to reach $1500 in 6 months, and is her surplus enough?
b)
She cuts entertainment by $60 and food out by $40 and saves the whole new surplus. Find her new surplus and the number of whole months she needs to save $1500.
c)
At the checkout, Ontario adds 13% HST to the shelf price. Can Aisha buy the laptop after 6 months? If not, how many months does she need?

Stuck? Peek at a hint

Surplus is net pay minus all expenses. Divide the goal by the number of months to get the monthly saving needed.

A2 Cards vs Snowmobile

A family in Timmins buys a hockey card collection for $2000 and a snowmobile for $12,000 in the same year. The cards appreciate by 9% each year. The snowmobile depreciates by 20% each year.

a)
Write an equation for the value of each item after $t$ years. Find each value after 5 years.
b)
Make a table of values for whole years. After how many years are the cards first worth more than the snowmobile?
c)
A dealer will always pay at least $500 for the snowmobile as parts. After how many years does the model first give a value below $500? What is the snowmobile worth from then on?

Stuck? Peek at a hint

An increase of 9% multiplies the value by $1.09$ each year; a decrease of 20% multiplies it by $0.8$ .

A3 Car Loan Choice

Ethan borrows $15,000 for a used car. Plan A: $463 a month for 36 months. Plan B: $256 a month for 72 months. The car loses 18% of its value each year.

a)
Find the total amount repaid and the cost of credit for each plan.
b)
Ethan picks Plan B because the payment is lower. How much more does Plan B cost in total? Find the car's value when Plan B is paid off.
c)
After 2 years on Plan B, Ethan wants to sell the car. The lender says he still owes $10,670. Find the car's value. Can selling it pay off the loan?

Stuck? Peek at a hint

Total repaid is the monthly payment times the number of months. The car's value follows $V=15000(0.82)^t$ .

Think It Through (T)

Error Analysis · Build a Budget

T1 Spot the Flaw

A student finds the value of $3000 invested at 6% per year, compounded annually, for 5 years:
"6% of $3000 is $180. Five years of interest is $5\times180=900$ , so the account holds $3900."

a)
What kind of interest did the student calculate? Find the correct value of the account.
b)
Find the interest earned during year 5 alone. Explain why it is more than $180.
c)
After how many whole years is the compound account first more than $500 ahead of the student's method?

Stuck? Peek at a hint

With compound interest, each year's interest is 6% of the balance at the start of that year.

T2 Build a Budget

Jordan's gross pay is $3000 a month, and deductions take 20%. Jordan's budget must follow three rules: rent is at most 35% of net income; savings is at least 10% of net income and is listed as an expense; the budget is balanced.

a)
Find Jordan's net income, the largest rent allowed and the smallest savings allowed.
b)
Write one balanced monthly budget for Jordan that follows all three rules and has at least two fixed and two variable expenses. Many answers are possible.
c)
When the lease renews, rent rises by 5%. Is the rent rule still met? Can cutting other expenses fix this? Find the smallest net income for which the new rent follows the rule.

Stuck? Peek at a hint

Find net income first: every rule is a percent of net income, not gross pay.

Boss Level

Optional challenge

Up, Then Down

A store raises the price of an item by a percent, then lowers the new price by the same percent.

a)
A jacket costs $80. Its price is raised by 25%, then the new price is lowered by 25%. Find the final price.
b)
For another item, a rise of $x\%$ followed by a fall of $x\%$ leaves the price 9% below the original. Find $x$ .
c)
Show that for every $x$ with $0<x<100$ , a rise of $x\%$ followed by a fall of $x\%$ ends below the original price.

Stuck? Peek at a hint

Write the two changes as multipliers, $(1+r)$ and $(1-r)$ , and multiply them.

Answer key

Final answers only. Try first, then check.

Core Skills

a) Fixed: rent, car insurance, phone plan. Variable: groceries, hydro, gas, entertainment.
b) Net income: $2510; expenses: $2110
c) Surplus of $400 a month; $4800 a year

a) $1389.15
b) $686.00
c) $25\%$ a year; $379.69

a) $300
b) $1894.50
c) $3\%$ per year

a) $2431.01
b) $431.01
c) $4187.42

a) $1326
b) $126
c) Total $1296, cost of credit $96; Plan 2 costs less

Real World

a) Surplus $172; she needs $250 a month, so no: she is $78 a month short.
b) Surplus $272; 6 months ($1632 saved)
c) No: the laptop costs $1695 with HST and she has $1632 after 6 months. She needs 7 months ($1904 saved).

a) Cards: $C=2000(1.09)^t$ , $3077.25; snowmobile: $S=12000(0.8)^t$ , $3932.16
b) After 6 years (cards $3354.20, snowmobile $3145.73)
c) After 15 years (model: $422.21). From then on it is worth about $500 as parts, so the model no longer applies.

a) Plan A: $16,668 repaid, $1668 cost of credit. Plan B: $18,432 repaid, $3432 cost of credit.
b) $1764 more; the car is worth $4560.10 after 6 years.
c) The car is worth $10,086. No: after selling it, Ethan still owes $584 and has no car.

Think It Through

a) Simple interest (interest on the $3000 only); correct value $4014.68
b) $227.25 ($4014.68 $-$ $3787.43). Year 5's interest is paid on the $3000 plus the interest from years 1 to 4.
c) After 10 years ($5372.54 compared with $4800)

a) Net income $2400; rent at most $840; savings at least $240
b) e.g. rent $840, phone $60, transit $130 (fixed); groceries $450, hydro $100, clothing $150, entertainment $170 (variable); savings $500. Total $2400.
c) New rent $882 > $840, so no. Cutting other lines keeps the budget balanced but does not change the 35% rule. Jordan needs a net income of at least $2520 (or cheaper rent).

Boss Level

Boss

a) $75
b) $x=30$
c) With $r=\frac{x}{100}$ , the price is multiplied by $(1+r)(1-r)=1-r^2$ , and $1-r^2<1$ because $r>0$ .

Free cheat sheet

Financial Literacy Cheat Sheet

The whole unit on one page: every rule, a worked example for each idea, and the traps that cost marks.

Unit Summary

One printable page with every rule.

↓ Unit Summary PDF

Build your own

The same page with blanks: fill it in from memory, then check.

↓ Build-your-own PDF

Phone card

The essentials on one screen. Save it to your photos.

↓ Phone card (image)

Most tested$3500 is invested at 4% per year, compounded annually, for 6 years. Find the amount and the interest earned. (card 5)

1Income and expenses

$\text{net}=\text{gross}-\text{deductions}$

UseBudget from net income (take-home pay). Needs are non-discretionary; wants (concerts, eating out) are discretionary.

Each month, the amount is:

the same	fixed: rent, insurance
different	variable: groceries, hydro

TrapGross $2600, deductions $520: budget the net $2080, not $2600.

2Surplus or deficit

UseSavings is a planned line, not whatever is left. One year: monthly amount $\times12$ .

Net income minus expenses (savings included):

positive	surplus
zero	balanced
negative	deficit: cut wants or earn more

ExampleNet $1850, expenses $1690: surplus $160 a month, $160\times12=1920$ a year.

TrapA $380 shelf price costs $380\times1.13=429.40$ with 13% HST: budget $429.40.

3Appreciation and depreciation

$\text{appreciation: }V=P(1+r)^t$

$\text{depreciation: }V=P(1-r)^t$

Use $P$ is the starting value, $r$ the yearly percent as a decimal (5% is $0.05$ ), $t$ the years. Compare two items at the same $t$ .

TrapLosing 20% a year for 5 years leaves $0.8^5\approx0.33$ of the value, not $0$ .

Trap$900 bike, down 30% a year: $900\times0.7^2=441$ after 2 years, not $900-270-270=360$ .

4Simple interest

$I=Prt\qquad A=P+I$

Use $r$ per year as a decimal, $t$ in years (9 months: $t=0.75$ ). To solve for one letter, divide $I$ by the other two: $r=I\div(Pt)$ .

Example$1500 at 6% for 2 years: $I=1500(0.06)(2)=180$ ; total $1680.

Trap$800 at 5% for 18 months: $I=800(0.05)(1.5)=60$ , not $800(0.05)(18)=720$ .

5Compound interest

$A=P(1+r)^t\qquad I=A-P$

$P=\dfrac{A}{(1+r)^t}$

UseCompounded annually: each year earns interest on the new balance. A goal later, money today: solve for $P$ .

Example$3500 at 4% for 6 years: $3500(1.04)^6\approx4428.62$ ; interest $928.62.

Trap$1000 at 8% compounded for 3 years: $1000(1.08)^3\approx1259.71$ , not $1000+3\times80=1240$ .

6Cost of credit

$\text{total}=\text{down}+n\times\text{payment}$

$\text{cost}=\text{total}-\text{price}$

Use $n$ is the number of payments (3 years monthly: $n=36$ ). Compare plans by total cost.

Example$900 TV, $100 down + 24 payments of $38: total $1012, cost of credit $112.

Trap48 payments of $300 total $14 400, more than 30 payments of $410 ($12 300).

Trap$200 down plus 12 payments of $80 is $1160 in total, not $960.

7Plan a goal

UseSurplus from net income; goal price with 13% HST; months $=$ goal $\div$ saving, rounded up.

Example$900 + HST is $1017; at $160 a month, $1017\div160\approx6.4$ , so 7 months.

TipAt 5% a year, $1000 becomes $2653 in 20 years, $7040 in 40.

TrapA $20 000 car, down 18% a year, is worth $13 448 after 2 years: maybe less than the loan.

Which formula?

Interest on the principal only

I=Prt

Interest on interest, or a value appreciates

P(1+r)^t

A value depreciates each year

P(1-r)^t

↓ Worksheet PDF ↓ Answer key PDF

Google Classroom Email

More free MTH1W worksheets

Other courses

All MTH1W resources → · All free resources →

What is VertexMath?

VertexMath is daily math practice for Ontario high school students, with a tutor that asks questions instead of giving answers. These worksheets are free, whether or not you use it.

Visit vertexmath.ca →