Simple vs Compound Interest Comparator
Side-by-side: simple, compounded and continuously-compounded growth.
Overview
A simple-versus-compound interest comparator puts three growth models side-by-side: simple interest, periodic compound interest, and continuous compounding. Simple interest pays the same dollar amount each period because the base never changes. Compound interest reinvests each period's interest, so the base grows and so does the interest. Continuous compounding is the mathematical limit as compounding frequency approaches infinity — every instant of accrual is reinvested immediately.
Visualizing the three growth paths at once is the fastest way to internalize why compounding matters for long horizons. Over one year the three are nearly indistinguishable; over thirty years at a modest rate the compounded curve doubles and triples the simple line. Compounding frequency itself is a smaller effect than people expect — quarterly versus monthly versus continuous, at the same nominal rate, produces only a few percent difference even over decades.
How it works
Simple interest: A = P × (1 + r × t), where P is principal, r is the annual rate, and t is years. Periodic compound interest: A = P × (1 + r/n)^(n × t) with n compounding periods per year. Continuous compounding: A = P × e^(r × t). Effective annual rate (APY) for periodic compounding is (1 + r/n)^n − 1. The comparator shows year-by-year balances for each model and the running gap between them, plus the final-year totals and APYs.
Examples
- $10,000 at 5% for 10 years: simple = $15,000; annual compound =
10,000 × 1.05^10 ≈ $16,289; continuous =10,000 × e^0.5 ≈ $16,487. The compound paths gain about $1,300–$1,500 over simple. - $10,000 at 5% for 30 years: simple = $25,000; annual compound =
10,000 × 1.05^30 ≈ $43,219; continuous =10,000 × e^1.5 ≈ $44,817. The compound paths nearly double simple. - $1,000 at 10% for 50 years: simple = $6,000; continuous =
1,000 × e^5 ≈ $148,413— the difference is two orders of magnitude. - 12% nominal rate compounded monthly vs continuously: APY is 12.68% versus 12.75% — under 0.1% difference per year despite the conceptual gulf.
FAQ
Why is APY always higher than the nominal rate?
Because earned interest gets reinvested. The more frequent the compounding, the bigger the gap, up to the continuous limit.
Does any real account compound continuously?
Practically no, but the formula is a tight upper bound and is widely used in derivatives pricing.
When is simple interest used in practice?
Some short-term loans, certain bond accrued interest conventions, and most cash-advance products.
Does inflation work the same way?
Yes. Inflation is a compound erosion of purchasing power — a 3% rate halves real value in roughly 24 years.
What's the most powerful lever for compound growth?
Time. Doubling the horizon usually beats doubling the rate.