Simple and compound interest
Principal, rate and term; simple interest (arithmetic sequence) and compound interest (geometric sequence), future value, proportional and equivalent rates, doubling time.
- 25 cards
- 4 topics
- Free
The outline, topic by topic
Each topic is weighted the way the exam weighs it.
- Concepts
- Questions
- The numbers
- The curves
A few cards from the deck
Interest rate: what is it?
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The ratio between what a sum lent or invested earns over one period and that sum: 5% a year means €5 for every €100 in one year.
A rate only means something with its period: 1% a month and 1% a year are very different. It must always be tied to the period it applies to.
€2,000 is invested for 3 years at 4% a year at simple interest. What is the future value?
- €2,240
- €2,249.73
- €2,480
- €2,120
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€2,240
Each year earns 2,000 × 0.04 = €80, so €240 over 3 years: €2,240. The €2,249.73 is the compound figure (2,000 × 1.04³).
A … rate is obtained by dividing the annual rate by the number of periods; an … rate gives, compounded over the year, the same final sum.
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A proportional rate is obtained by dividing the annual rate by the number of periods; an equivalent rate gives, compounded over the year, the same final sum.
At 12% a year, the proportional monthly rate is 1% (12 ÷ 12) but it would earn 12.68% over the year: the equivalent rate, which is lower, is 0.95%.
Simple interest: what is it?
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A regime where the earnings are always computed on the starting sum: they are the same each period and grow in proportion to time.
The future value is C × (1 + i × n): an arithmetic sequence with common difference C × i, so a straight line when plotted against time.