Compound interest pays interest on interest, so the growth curve bends upward rather than running in a straight line. Set a starting balance, an optional monthly contribution, a rate and a term to see the final balance split into what you put in and what the interest added.
Simple interest pays only on the original sum, so it grows in a straight line. Compound interest pays on the balance, including interest already earned, so each period starts from a bigger base. Over short periods the difference is trivial. Over decades it dominates: the interest-on-interest component eventually exceeds everything you contributed.
Divide 72 by the annual rate to estimate the years needed to double your money. At 6% that is twelve years, at 9% eight. It is accurate enough for mental arithmetic anywhere between about 4% and 12%, and it is a fast sanity check on any investment claim.
The figures here ignore inflation and tax. To think in today's purchasing power, subtract expected inflation from the rate before you start: 7% nominal growth with 3% inflation is closer to 4% real. Over 30 years that distinction is the difference between a plausible plan and a fantasy.
For a lump sum, A = P(1 + r/n)^(nt), where P is the principal, r the annual rate, n the number of compounding periods per year and t the number of years. Regular contributions add a future-value-of-an-annuity term on top.
Less than most people expect. At 6% for 10 years, annual compounding turns 10,000 into 17,908 and daily compounding into 18,220 - a difference of under 2%. The rate and the time horizon matter far more than the frequency.
No, the result is a nominal figure. To think in today's money, subtract expected inflation from the rate: 7% growth with 3% inflation is roughly 4% in real terms.
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