Grade 10 · Grade 10: Exact Values and Financial Mathematics · Exact Values and Financial Mathematics
Exact Values and Financial Mathematics
Choose exact or approximate form wisely, then model interest, appreciation, depreciation and inflation.
Learning objectives
- Work fluently with surds, rational exponents and exact trigonometric values.
- Solve simple and compound interest problems.
- Model appreciation, depreciation and inflation exponentially.
- Decide when exact form matters.
AERO Mathematics alignment
AERO.M10.NS.1
Work fluently with surds, rational exponents and exact values, choosing exact or approximate forms appropriately.
AERO.M10.NS.2
Solve problems involving simple and compound interest, appreciation, depreciation and inflation using exponential models.
MYP criteria
- Criterion A — Knowing and understanding
- Criterion C — Communicating
- Criterion D — Applying mathematics in real-life contexts
ENGAGE
Start here
You invest 10 000 QAR at 6% for 4 years, once as simple interest and once compounded annually.
Think about it
How much more does compounding earn, and why does the gap grow over time?
Hint: Compound interest earns interest on previous interest.
EXPLAIN
Exact values and money over time
Choosing exact or approximate
Exact values such as √3/2 and π/4 keep every digit of accuracy through a calculation. Convert to decimals only at the end, and round to a precision the context supports.
Simple and compound interest
| Model | Formula | Value after 4 years on 10 000 at 6% |
|---|---|---|
| Simple | A = P(1 + rt) | 12 400 |
| Compound annually | A = P(1 + r)ᵗ | 12 624.77 |
| Depreciation | A = P(1 − r)ᵗ | Falls each year |
Compounding earns interest on interest, so the gap widens every year. Over 20 years the same rate produces a dramatically different result.
Inflation and real value
Inflation is exponential decay in purchasing power. At 3% inflation, 100 QAR buys what 100 × 0.97ᵗ would buy today after t years.
Where this is used
Savings accounts, car depreciation, loan repayments and long-term planning all rest on exponential models.
INVESTIGATION
Try it yourself
Compare two real savings or loan offers with different rates and compounding periods. Build a table over 10 years and state which offer wins and by how much.
Watch
Exponential Growth and Decay Word Problems
Khan Academy · 7:21
Compound interest is exponential growth with money.
Before you watch: Which is larger after 10 years: 5% simple or 5% compound?
- Find the value of 10 000 after 4 years at 6% compounded annually.
- A car depreciates 15% per year. What is left after 3 years?
Interactive simulation · PhET
Function Builder
Build a machine that multiplies by 1.05 repeatedly to model compound growth.
While you explore
- After how many steps does the value double?
- How does compound interest differ from simple interest?
Key vocabulary
- Depreciation
- The loss of value of something over time.
- Compound interest
- Interest earned on your interest as well as your original money.
Practice questions
0/1 correct
Level 1 · Criterion A
Find the value of 8000 QAR after 3 years at 5% compounded annually.
MYP criterion tasks
Level 2 · Criterion D
A car worth 90 000 QAR depreciates 15% per year. Find its value after 4 years and explain why it never reaches zero.
Reflect & track
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