Compound interest and depreciation

Change the principal, rate, compounding frequency and time to compare simple, compound and continuous models, for growth or for depreciation. Drag across the graph to read the value at any time.

Drag on the graph, or focus it and use ← / → (Shift for 0.1 year steps).

Mode

Principal P

Annual rate r

Periods per year n

Time t

Try this

Set r = 12 % and t = 10 years. Step n from 1 to 365 and watch the compound value approach, but never pass, the continuous value.
In growth mode at r = 8 %, read the doubling time, then check it against the rule of thumb 72 ÷ 8 = 9 years.
Switch to depreciation with r = 15 %, n = 1: find the year in which the straight-line (simple) model reaches zero while the compound model is still positive.

Exam tip: write r as a decimal and count the exponent in periods (monthly for 5 years gives nt = 60), keep full calculator values until the end, then give money to 2 decimal places.

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More on 1: Arithmetic and geometric series · Proof by induction · Permutations and combinations · De Moivre's theorem · Systems of linear equations

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