Interest & Savings
Interest & Savings is a free interactive simulation from StudyFi Lab. It runs right in your browser, with no sign-up and nothing to install.
Watch savings grow: simple vs compound interest, solve any unknown
Experiments
Simple vs compound interest
With simple interest, interest is only ever paid on the original deposit: u = G₀ · p · t. With compound interest, each period’s interest joins the balance and earns interest itself: Gₙ = G₀ · rⁿ, where r = 1 + i is the growth factor per period and n = m · t the number of periods. School mode uses the conformal rate i = (1 + p)^(1/m) − 1, so a year still yields exactly p; bank mode divides, i = p / m, and yields slightly more. The 15 % tax is withheld from every interest payment, so r = 1 + i · (1 − 0.15); days are counted in a 365-day year.
Try this: Set 8 % for 3 years and guess the gap before you check. Then stretch the time to 30 years — the gap outgrows the simple interest itself.
Solve for the unknown
The formula Gₙ = G₀ · rⁿ links four quantities: know three and you can work out the fourth. The principal is G₀ = Gₙ / rⁿ, the time needs a logarithm, n = ln(Gₙ / G₀) / ln r, and the rate needs the n-th root, r = ⁿ√(Gₙ / G₀). The number of periods is n = m · t, with m compounding periods per year; days convert with a 365-day year.
Try this: Pick t as the unknown and set Gₙ to one and a half times the principal at 3 % p.a. How long does it take with annual and with monthly compounding?
Rule of 72
Money doubles when rⁿ = 2, so the exact doubling time is t = ln 2 / (m · ln r). For everyday rates a quick estimate does the job: t ≈ 72 / p, with p in percent. The chart shows how good the estimate is: it fits best around 8 % and drifts further off for very low or very high rates.
Try this: Find the rate where the two curves cross. Then switch the tax on — how many years later does the money double?
Frequently asked questions
What is Interest & Savings?
Interest & Savings is a free interactive simulation from StudyFi Lab. It runs right in your browser, with no sign-up and nothing to install. Watch savings grow: simple vs compound interest, solve any unknown
Is Interest & Savings free?
Yes. Interest & Savings is completely free. It works in the browser on computers, tablets and phones, and you do not need an account.
What can I explore in Interest & Savings?
Simple vs compound interest, Solve for the unknown, Rule of 72.
What does the “Simple vs compound interest” experiment show?
With simple interest, interest is only ever paid on the original deposit: u = G₀ · p · t. With compound interest, each period’s interest joins the balance and earns interest itself: Gₙ = G₀ · rⁿ, where r = 1 + i is the growth factor per period and n = m · t the number of periods. School mode uses the conformal rate i = (1 + p)^(1/m) − 1, so a year still yields exactly p; bank mode divides, i = p / m, and yields slightly more. The 15 % tax is withheld from every interest payment, so r = 1 + i · (1 − 0.15); days are counted in a 365-day year.
What does the “Solve for the unknown” experiment show?
The formula Gₙ = G₀ · rⁿ links four quantities: know three and you can work out the fourth. The principal is G₀ = Gₙ / rⁿ, the time needs a logarithm, n = ln(Gₙ / G₀) / ln r, and the rate needs the n-th root, r = ⁿ√(Gₙ / G₀). The number of periods is n = m · t, with m compounding periods per year; days convert with a 365-day year.
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