How much does 3% grow over 48 years?

Question

A slow, steady account earns 3\% a year for 48 years. Solve in your head. Roughly how many times does the money multiply? Aim: under 15 seconds.

Accepted Answer

Doubling time first: \frac{72}{3} = 24 	ext{ years.} The 48-year horizon is exactly two doubling periods: \frac{48}{24} = 2 	ext{ doublings} \;\Rightarrow\; 2^{2} = 4	imes. Check: 1.03^{48} \approx 4.1. Takeaway. Pick horizons that are whole multiples of the doubling time and the compounding factor becomes a clean power of two, no fractional exponents needed. Even modest 3\% growth quadruples money over a working lifetime.

How much does 3% grow over 48 years?

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