Brain Teasers & Mental Math
At a 10% discount rate, roughly what fraction of a perpetuity's value is captured by just the first 30 years of cash flows?
Model answer
About 94%.
A 30-year annuity = perpetuity × (1 − 1/1.10³⁰). Estimate 1.10³⁰ mentally with the rule of 72: at 10%, money doubles every ~7.2 years, so 30 years ≈ 4+ doublings ≈ 17–18×. Then 1 − 1/17.5…
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