Percentages (II) · Ages 13–14
Compound interest
A = P × (1 + r%)n, interest = A − P.
How to do it
Method
A = P × (1 + r%)^n, interest = A − P
8000 × 1.053 = 9261
Another way
Year by year
8000 → 8400 → 8820 → 9261
In full
Compound interest adds each period's interest to the principal, and the next period's interest is on both. Compounded yearly, the amount after n years is A = P × (1 + r%)n, and the interest is A − P. $8000 at 5% a year for 3 years: one way, the formula, 8000 × 1.053 = 9261; another, year by year, 8000 → 8400 → 8820 → 9261. The interest is 9261 − 8000 = $1261. Simple interest on the same money at the same rate is only 8000 × 5% × 3 = $1200: the extra is interest earned on interest. Back from the amount to the principal: P = A ÷ (1 + r%)n. Where the answer is rounded, round at the last step only, never on the way.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
$27,000 at 10% a year, compounded yearly, for 4 years. The amount = $ (to the nearest dollar)
Show the answer and working
Answer: 39,531
Amount = 27000 × (1 + 10%)4 = 27000 × 1.14, about 39531. Round at the last step only.
Example 2
$20,000 at 2% a year, compounded yearly: the amount after 1 year is $, after 2 years $, after 3 years $.
Fill in each blank
Show the answer and working
Answer: 20,400, 20,808, 21,224.16
Times 1.02 each year: 20000 × 1.02 = 20400, 20400 × 1.02 = 20808, 20808 × 1.02 = 21224.16. Or in one step: 20000 × 1.023 = 21224.16.
Example 3
A principal of $8,000 at 4% a year, compounded yearly. Which expression gives the amount after 6 years?
- A. 8000 × (1 + 4% × 6)
- B. 8000 × 1.04 × 6
- C. 8000 × 0.046
- D. 8000 × 1.046
Choose the right answer
Show the answer and working
Answer: D. 8000 × 1.046
Each year the money becomes 1.04 times the year before; 6 years multiply 6 times: 8000 × 1.046.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.$2,000 at 2% a year, compounded yearly: the amount after 1 year is $, after 2 years $, after 3 years $.
Fill in each blank
Answer:
2.$30,000 at 6% a year, compounded yearly, for 6 years. The amount = $ (to the nearest dollar)
Answer:
3.$29,000 at 8% a year, compounded yearly, for 5 years: the compound interest = $ (to the nearest dollar)
Answer:
4.$8,000 at 8% a year for 4 years. How much more does interest compounded yearly earn than simple interest, to the nearest dollar?
- A. $2,560
- B. $10,884
- C. $324
- D. $2,884
Choose the right answer
Answer:
5.On $20,000 at 4% a year, compounded yearly, the interest for 5 years is about $4,000.
True or false?
Answer:
All the answers
- 1. 2,040, 2,080.8, 2,122.416
- 2. 42,556
- 3. 13,611
- 4. C. $324
- 5. False
VIP practice notes and papers
Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.
- Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
- Practice paper: Set out in parts like a school paper, marked, with answers and full working
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