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Practice sheet · Economy Path · Lens 1: Math

Percent & interest

Practice for The Math of the Economy: markets, elasticity, percentages, inflation, interest, GDP and budgets (pp.8–16), plus the Algebra Level Up (pp.17–18). Maths practice, not financial advice.
Warm-upCoreLevel Up
Name Date Time I spent
Remember

Percent of what? % change = (new − old) ÷ old × 100. A rate going from 2% to 3% rose 1 percentage point, but 50 percent (p.11).

Compound interest: A = P(1 + r)t. Each year earns interest on the interest. Rule of 72: years to double ≈ 72 ÷ the rate (p.13). All prices and rates here are made-up examples.

Warm-up

One step

Percent change, points and the rule of 72.
1

Lunch price

A school lunch goes from $8.00 to $8.60. What is the percent change?

2

Points or percent?

A made-up interest rate rises from 2.25% to 2.75%. How many percentage points is that? What percent rise is it?

3

Up 10, down 10

A $50 game goes up 10%, then that new price goes down 10%. What does it cost now? Why isn’t it $50?

4

Rule of 72

About how many years does money take to double at 9% a year? Check with a calculator: what is 1.09⁸?

Core

Two or three steps

Say what the base is before you divide.
5

A real raise?

Your pay rises 4% this year while prices (CPI) rise 3%. Find the real change in what you can buy, to two decimal places (p.12).

6

Simple or compound?

$500 earns 4% a year for 3 years. What do you have with simple interest? With compound interest? What is the difference?

Percent Practice · Economy Path · Unizon1/2
Economy Path · Unizon · PracticePercentages & interest
7

Stretchy or stiff?

A café raises a muffin from $2.00 to $2.20 and sales fall from 100 to 95 a day. Find the elasticity. Elastic or inelastic? What happens to revenue?

8

A $450 month

Use the 50/30/20 starting point (p.16) on $450. How much for needs, wants and savings? Name one reason it might not fit someone.

9

Too cheap

Rinkside Cocoa (p.17): Qd = 120 − 20p and Qs = 20p. At a price of $2.50, how many cups do buyers want and sellers offer? Is there a shortage or a surplus, and how big?

10

Island GDP

A fictional island: consumers $800M, investment $200M, government $300M, exports $150M, imports $250M. Find GDP = C + I + G + (X − M) and GDP per person for 30,000 people.

Level Up

Equations and exponents

From A1–A2 (pp.17–18). Use a calculator for powers and roots.
11

Solve for equilibrium

A market has Qd = 150 − 25p and Qs = 25p − 50. Set them equal and solve for the price and the quantity. Check by substituting.

12

Five years at 6%

Find A = 1,000 × 1.06⁵ to the cent. How much of it is interest?

13

Work backwards

You want $3,000 in 8 years at 4% a year. Solve 3,000 = P × 1.04⁸ for what you need today.

14

Find the rate

$2,000 grew to $2,163.20 in 2 years with compound interest. Solve 2,000(1 + r)² = 2,163.20 for r. Why drop the negative root?

Make your own problem

Your turn to be the economist

  1. Find a real price, rate or headline (a flyer, a bus fare, a news story).
  2. Write a percent, interest or budget question about it with the base made clear.
  3. Solve it, then rewrite the headline so it says “from ___ to ___”.

My problem, and my worked answer:

Percent Practice · Economy Path · Unizon2/2
Economy Path · Unizon · PracticePercentages & interest

Try every problem first, then check here. Wrong answers are useful: find the step where your work and the key split apart.

The key never prints with Print my work or Print blank. Open it to get its own Print the answer key button.

Answer key

Worked solutions. Money answers are rounded to the cent. Maths practice only, not financial advice.

Warm-up
1
+7.5% (8.60 − 8.00) ÷ 8.00 × 100 = 0.60 ÷ 8 × 100 = 7.5%.
2
0.5 points · ≈ +22.2% 2.75 − 2.25 = 0.5 points. 0.5 ÷ 2.25 × 100 ≈ 22.2%.
3
$49.50 50 × 1.10 = $55. 55 × 0.90 = $49.50. The 10% off is 10% of $55, a bigger base.
4
≈ 8 years · 1.99 72 ÷ 9 = 8. 1.09⁸ ≈ 1.99: almost exactly double.
Core
5
≈ +0.97% 1.04 ÷ 1.03 − 1 ≈ 0.0097 = 0.97%. You can buy a little more, but less than the 4% suggests.
6
$560 · $562.43 · $2.43 Simple: 500 × 0.04 × 3 = $60, so $560. Compound: 500 × 1.04³ = $562.43. The extra $2.43 is interest on interest.
7
−0.5 · inelastic · up to $209 Price +10% (0.20 ÷ 2.00); sales −5% (5 ÷ 100). −5 ÷ 10 = −0.5: smaller than 1, inelastic. Revenue 2.00 × 100 = $200 → 2.20 × 95 = $209.
8
$225 · $135 · $90 450 × 0.5, × 0.3, × 0.2. It doesn’t fit everyone: someone with high rent may need far more for needs (p.16).
9
70 · 50 · shortage of 20 Qd = 120 − 20 × 2.5 = 70. Qs = 20 × 2.5 = 50. Buyers want 20 more than sellers offer: a shortage.
10
$1,200M · $40,000 800 + 200 + 300 + (150 − 250) = 1,200. $1,200,000,000 ÷ 30,000 = $40,000 per person.
Level Up
11
p = $4 · Q = 50 150 − 25p = 25p − 50 → 200 = 50p → p = 4. Check: 150 − 100 = 50 and 100 − 50 = 50.
12
$1,338.23 · $338.23 1.06⁵ ≈ 1.338226, so A ≈ $1,338.23, of which $338.23 is interest.
13
P ≈ $2,192.07 1.04⁸ ≈ 1.368569. P = 3,000 ÷ 1.368569 ≈ $2,192.07.
14
r = 4% (1 + r)² = 2,163.20 ÷ 2,000 = 1.0816 → 1 + r = √1.0816 = 1.04 → r = 0.04. The other root, 1 + r = −1.04, makes no sense for money.
Make your own: say what the base is, label rates as percent or percentage points, and remember that real returns are never guaranteed.
Percent Practice · Economy Path · UnizonAnswer key