Money grows as $dP/dt = 0.05P$ (5% continuous interest). A friend says: "It grows by the same amount every year." What is the truth?

Hints

The rate is proportional to the current balance $P$ , not the starting one.
A bigger balance earns bigger interest, which builds a bigger balance… that feedback is the signature of $e^{kt}$ .

Show the answer

B. It grows by the same percentage each year

Why

Proportional rate means exponential growth: $P = P_0e^{0.05t}$ . Fixed percentage, compounding absolute gains, the same law behind population booms, radioactive decay (with $k<0$ ) and epidemic take-offs.

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Money grows as dP/dt=0.05PdP/dt = 0.05PdP/dt=0.05P (5% continuous interest). A friend says: "It grows by the same amount every year." What is the truth?

Practise Differential models in one variable

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Money grows as $dP/dt = 0.05P$ (5% continuous interest). A friend says: "It grows by the same amount every year." What is the truth?