Comparison of simple and compound

For the same capital and rate, the two regimes start almost neck and neck but diverge ever more as the years pass. A numerical comparison makes it clear why.

Example — Comparison over 10 years

$C_0 = 1000$ EUR at $5\%$ per year.

• Simple: $M_{10} = 1000\cdot(1+0{,}05\cdot 10) = 1500$ EUR (interest $500$).
• Compound: $M_{10} = 1000\cdot 1{,}05^{10} \approx 1628{,}89$ EUR (interest $\approx 629$).

Over $40$ years the difference explodes: $M_{40}^{\text{sempl}} = 3000$, $M_{40}^{\text{comp}} = 1000\cdot 1{,}05^{40} \approx 7039{,}99$. Compound capitalisation is the engine of long-term investments and — mirror-wise — of debts that worsen if not repaid.

At $10$ years the gap is modest; at $40$ years the compound amount is more than double the simple one. Exponential growth works in favour of those who invest and against those who accumulate debts.

Links

Topics: Percentages
Concepts: Exponential growth · Compound interest · Simple interest
Methods: Compound interest · Simple interest
Skills: Calculating · Estimating