The Mathematics of Fixed Deposits: Compounding Frequency, Tax-Drag, and Real Purchasing Power Preservation
Fixed Deposits (FDs) and Recurring Deposits (RDs) form the conservative core of wealth management. However, nominal interest rates advertised by commercial banks fail to account for two destructive forces: periodic compounding yield drift, income tax brackets, and macroeconomic inflation erosion. Below is the quantitative architecture of fixed-income yield analysis.
1. The Quarterly Compounding Equation & Effective Annual Rate
In most global commercial banks, fixed deposit interest is compounded quarterly (n = 4). Because accrued interest is reinvested every 3 months, the Effective Annual Rate (EAR) or Annual Percentage Yield (APY) exceeds the nominal stated APR.
A = Final maturity proceeds at tenure completion.
P = Initial principal deposit amount.
r = Stated nominal annual interest rate (e.g. 0.071 for 7.1%).
n = Compounding frequency per year (n = 4 for quarterly, n = 12 for monthly).
t = Investment horizon in years.
2. Post-Tax Drag and the Fisher Real Return Equation
The primary risk facing fixed-income depositors is not credit default (which is insured by deposit insurance corporations), but purchasing power decay. Under the Fisher Equation, the real rate of return rreal is:
( 1 + rnominal, post-tax ) = ( 1 + rreal ) × ( 1 + iinflation )
If a bank pays 7.0% interest and the depositor sits in a 30% tax bracket, the post-tax return is 4.90%. If annual CPI inflation is 5.50%, the real purchasing power return is -0.57% per year. Fixed deposits preserve nominal principal, but lose real purchasing power over long horizons.