Video coming soon. The lesson video will appear here once it is published on YouTube.
In this lesson you learn to
- Explain the difference between simple and compound interest
- Use the formula start × (1 + rate)^years
- Estimate doubling time with the rule of 72
- Recognise the unsupported Einstein quote
- Describe what happens when interest is added more and more often
- Explain why starting later costs the last, fastest years
- Apply the same math to a debt that grows
Key points
- Simple interest is figured on the starting amount only; compound interest on the growing balance.
- With 1,000 at 5 percent for 30 years: simple 2,500, compound 4,321.94 (worked example).
- Final amount = start × (1 + rate)^years.
- Rule of 72: years to double ≈ 72 ÷ rate in percent (an approximation).
- No solid evidence that Einstein called compound interest the eighth wonder of the world.
Quiz
Choose an answer to see whether it is right and why. Example numbers are worked examples, not predictions.
Sources (9)
- Quote Investigator: The Eighth Wonder of the World Is Compound Interest (2019)
- Quote Investigator: Compound Interest Is Man's Greatest Invention (2011)
- e (mathematical constant), history section (Wikipedia, signpost only)
- Rule of 72 (Wikipedia, signpost only); primary source: Luca Pacioli, Summa de arithmetica, Venice 1494, f. 181
- Own calculation: K(t) = K0 × (1 + r)^t, yearly compounding, no withdrawals, no taxes or fees
- MacTutor (University of St Andrews): A Napierian logarithm before Napier (Pacioli, Summa de arithmetica 1494, fol. 181, n. 44)
- MacTutor: Jacob Bernoulli (biography)
- MacTutor (University of St Andrews), J J O'Connor and E F Robertson: The number e (September 2001)
- Benjamin Franklin, codicil of 23 June 1789 (Wikisource transcript; date confirmed via Founders Online)
Education only. Not financial advice.