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For Students · Markov Chains

Markov Chains for compound interest

Built for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition. Simulate compound interest live below — adjust the inputs and watch it respond, right in your browser.

Markov ChainLive

transitions → stationary distribution

A100.0%

B0.0%

C0.0%

Controls

A system hops between states by fixed probabilities. From any start it converges to the same stationary distribution — the math behind PageRank and queueing.

Presets

Stay in A

Stay in B

Stay in C

▶ Run in Python

Data Inspector

Step0

P(A)1.000

P(B)0.000

P(C)0.000

Governing equation

x_{t + 1} = P x_{t}, π P = π, P = 0.7 0.20 0.25 0.15 0.6 0.25 0.15 0.20 0.5

Reading this result: State A has the stickiest self-loop (0.70), so it keeps the largest share of the stationary distribution no matter where you start.

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Frequently asked questions

Is this good for students?: Yes — this version of "Markov Chains for compound interest" is framed for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.