Archive / Investment Adviser (Level 1) / Evaluating the Financial Position of Clients

nism-series-xa-rule-of-72-doubling-time-calculation[ INVESTMENT ADVISER (LEVEL 1) ]

Using the standard financial planning 'Rule of 72', approximately how many years will it take for a lumpsum investment to double in value at a compounded annual return of 7.2% p.a.?

[ A ]Approximately 13.9 years (100 / 7.2)

[ B ]Approximately 5.0 years

[ C ]Approximately 10.0 years (72 / 7.2)[ CORRECT ]

[ D ]Approximately 20.0 years

Takeaway

Option C is correct: Approximately 10.0 years (72 / 7.2)

Derivation

Rule of 72 provides a quick mental estimate of doubling time: divide 72 by the annual compounded return. Doubling Years ≈ 72 / 7.2 = 10.0 years. Unlike the simple linear shortcut of dividing 100 by the rate (100 / 7.2 ≈ 13.9 years, which would apply if growth were non-compounding), the Rule of 72 is specifically calibrated to approximate compound growth, and it stays remarkably accurate across a wide band of realistic annual return rates, typically 6% to 10%. It becomes progressively less precise at very high or very low rates, but for a scenario like 7.2%, where 72/7.2 divides out to a clean 10, it is essentially exact.

Why the others fail

A — Approximately 13.9 years (100 / 7.2)

Uses simple linear division (100 divided by the rate) rather than the compounding-calibrated Rule of 72, which is the formula actually being tested here.

B — Approximately 5.0 years

5.0 years is far shorter than what a 7.2% compounded annual return would actually take to double an investment, based on the Rule of 72 calculation.

D — Approximately 20.0 years

20.0 years is roughly double what the Rule of 72 calculation actually yields for a 7.2% compounded annual return, overstating the true doubling time.