Archive / Investment Adviser (Level 2) / Life Insurance Products

nism-series-xb-geometric-real-rate-formula-versus-simple-subtraction[ INVESTMENT ADVISER (LEVEL 2) ]

In Human Life Value and retirement discounting, why is the exact geometric inflation-adjusted formula: 'Rate = ((1 + r) / (1 + i)) - 1' used instead of simple subtraction '(r - i)'?

[ A ]Simple subtraction is banned by the Income Tax Department

[ B ]The geometric formula always produces a negative interest rate

[ C ]Simple subtraction only applies to US Dollar calculations

[ D ]Geometric compounding accurately accounts for the simultaneous inflation growth of expenses/income and the compound reinvestment yield of the corpus, preventing substantial compounding estimation errors over multi-decade horizons[ CORRECT ]

Takeaway

The geometric formula is used because inflation and investment returns compound simultaneously, and simple subtraction produces significant estimation errors over multi-decade horizons, so option D is correct.

Derivation

Both the income/expense stream and the investment return compound year over year, so their net real effect must also be derived through compound (geometric) division, not linear subtraction. Over short periods the two approaches converge closely, but over 20-30 year horizons the gap widens materially — for example, simple subtraction of 10% - 6% gives 4%, while the exact geometric rate ((1.10)/(1.06)) - 1 = 3.7736% is meaningfully lower, and this gap compounds further when raised to a high power in a PV/FV calculation. This tests the mathematical reasoning behind why NISM's exact real-rate formula, not the popular shortcut, is the standard used throughout retirement and HLV calculations.

Why the others fail

A — Simple subtraction is banned by the Income Tax Department

Mathematical discounting formulas are actuarial and financial planning tools; they are not banned or regulated by the Income Tax Department.

B — The geometric formula always produces a negative interest rate

The geometric formula produces a positive real rate whenever the nominal return exceeds inflation; it does not always produce a negative rate.

C — Simple subtraction only applies to US Dollar calculations

Geometric compounding is a universally applicable mathematical technique and is not restricted to US Dollar-denominated calculations.