N3 · Compound Interest Year by Year

Alberta Grade 11 Mathematics

Number and money

How interest can earn more interest over time

What you will learn

• Explain how compound interest differs from interest calculated only on the starting amount.
• Identify the principal, annual rate, compounding frequency, and time in an interest problem.
• Calculate a compound-interest balance and the interest earned.
• Check whether an answer is reasonable and report money to the nearest cent.

From a starting amount to compound growth

• Compound interest is calculated on the current balance, including previously added interest.
• The balance grows by adding the interest for the period to the current balance.
• Use the rate and compounding schedule stated in the problem.

Build the compound-interest model

• Convert the annual percent rate to a decimal before using it.
• Use the frequency and time together to count all compounding periods.
• Do not mistake the annual rate for the rate in each month or quarter.

Plan the work and check the answer

• Write down what each given number represents before substituting.
• Check that the balance exceeds the principal when the rate and time are positive.
• Use subtraction to confirm the interest earned.

Try it: identify, calculate, check

• The model depends on entering values with matching meanings and units.
• A final check can catch a wrong period count, a misplaced decimal, or an answer to the wrong question.

Counting compounding periods

Worked example

Annual compounding

1. Identify the values
   The principal is CAD 800. Change the annual rate of 4% to the decimal 0.04. Interest is added once each year, so there are three periods in three years.
   $$P=800,\quad r=0.04,\quad n=1,\quad t=3$$
2. Calculate the balance
   Use one annual growth factor for each of the three years. The result is the full balance, including the principal and interest.
   $$A=800(1+0.04)^3\approx 899.89$$
3. Find the interest earned
   Subtract the original principal from the final balance. The answer is rounded to the nearest cent.
   $$899.89-800=89.89$$

Worked example

Monthly compounding

1. Match the rate to the periods
   The annual rate is 6%, or 0.06 as a decimal. Monthly compounding has 12 periods per year. Over two years, that gives 24 periods.
   $$P=1200,\quad r=0.06,\quad n=12,\quad nt=24$$
2. Calculate the balance
   Divide the annual decimal rate by 12 to find the rate for one month. Apply that monthly growth factor 24 times, then round the final balance to the nearest cent.
   $$A=1200\left(1+\frac{0.06}{12}\right)^{24}\approx 1352.59$$
3. Calculate interest earned
   Subtract the starting amount from the balance. This difference is the total interest added over the two years.
   $$1352.59-1200=152.59$$

Worked example

Compare two compounding schedules

1. Calculate annual compounding
   Annual compounding adds interest once per year. Four years therefore gives four periods. Use the annual decimal rate of 0.03.
   $$A=2000(1+0.03)^4\approx 2251.02$$
2. Calculate quarterly compounding
   Quarterly compounding means four periods each year. Over four years there are 16 periods. Divide the annual decimal rate by four for each period.
   $$A=2000\left(1+\frac{0.03}{4}\right)^{16}\approx 2253.98$$
3. Compare the balances
   The principal, annual rate, and time are the same in both calculations. Quarterly compounding gives a slightly higher balance because interest is added more often.
   $$2253.98-2251.02=2.96$$

Common mistakes and how to avoid them

Lesson summary

• Compound interest is calculated on the current balance, including earlier interest.
• Convert the annual rate from a percent to a decimal and match it to the compounding frequency.
• Use the compound-interest model to calculate the final balance.
• Subtract the principal from the final balance when asked for interest earned.
• Check units, rounding, and whether the result makes sense.

Check your understanding

Key terms

Principal

The starting amount of money in an interest calculation.

Interest

Money added to an account based on its balance and an interest rate.

Rate

A percent that tells how much interest is added over a stated time period.

Compounding period

The time between additions of interest to an account.

Balance

The amount of money in an account at a particular time.

Growth factor

The multiplier used to change a balance from one compounding period to the next.

Continue through Math 20-3

View the complete Math 20-3 Alberta Grade 11 Mathematics curriculum and lessons

• N1 · Use and verify strategies for numerical puzzles and games
• N4 · Compare services used to access and manage finances
• N5 · Compare credit-card and loan options in context
• M2 · Solve volume and capacity problems with SI and imperial units
• G1 · Solve problems involving two or three right triangles
• G2 · Solve practical scale and scale-diagram problems

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About this lesson and its review

Published by DoAssignment. This reviewed lesson follows Alberta Grade 11 Mathematics (Math 20-3), expectation N3. It is a study resource, not an official curriculum publication.

Before publication, content is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability. Errors can still occur, so corrections are welcomed.

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