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Finance, investment, and planning calculations — explained and demystified.
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Flat Rate vs Reducing Balance: The Same 7% Costs Double
Why 31 January Plus One Month Has No Right Answer
Adding one month to 31 January has no correct answer, and "add one day" isn't "add 24 hours". The date arithmetic edge cases that break calendars and billing systems.
Your Fixed Deposit Is Only Guaranteed Up to a Point
Deposit protection is per banking licence, not per brand — and it includes accrued interest. Two ways a large fixed deposit ends up partly unprotected by accident.
Why a 25% Average Return Can Leave You With Nothing
An investment can average 25% a year and return nothing. Here's the gap between arithmetic and geometric means, why volatility drags compound growth, and sequence risk.
Why Salary Sacrifice Beats a Regular Pension Contribution — NI Savings, Employer Passthrough, and the £100,000 Taper
Salary sacrifice reduces gross salary before both income tax and National Insurance are calculated — unlike relief-at-source pensions which only save income tax. An employee on £40,000 sacrificing £4,000 saves £320 in NI on top of income tax relief, and their employer saves £552 in employer NI which many pass on to the employee's pension. Here's the full calculation, the personal allowance taper at £100,000, and what salary sacrifice reduces (statutory pay, mortgageable income) versus what it doesn't.
Why the Entire Money Market Uses Simple Interest — T-Bills, Day Count Conventions, and the Rule of 78s
The entire money market — Treasury bills, commercial paper, repos, and the Fed Funds Rate — uses simple interest, not because it's simpler but because the compounding period would need to be fractions of a day for instruments measured in weeks. Here's how day count conventions (Act/360, Act/365, 30/360) affect interest calculations by enough to matter in the inter-bank market, the discount rate vs investment yield distinction that makes T-bill comparisons tricky, and why the Rule of 78s front-loads interest at the expense of early repayers.
A ₹10 NAV Fund Isn't Cheaper Than a ₹500 NAV Fund — The NAV Misconception and What Actually Predicts Fund Quality
A fund with NAV ₹10 is not cheaper or better value than a fund with NAV ₹500 — NAV is total assets divided by units outstanding, reflecting fund age and accumulated history, not future return potential. Here's the worked example showing identical percentage returns regardless of NAV level, the metrics that actually predict fund quality (expense ratio, manager tenure, AUM appropriateness), and why direct plans' lower expense ratio compounds to a meaningful difference over a 20-30 year SIP horizon.
Two Retirees, Same Average Return, Completely Different Outcomes — Sequence of Returns Risk Explained
Two retirees with identical average 7% returns over 25 years can have dramatically different outcomes purely based on when the bad years occurred — withdrawing during a market decline permanently removes capital that can never participate in the eventual recovery. Here's the mathematics of why sequence matters more than average, the "retirement red zone" concept, the bucket strategy that protects near-term spending from market timing, and how annuitisation eliminates sequence risk entirely for essential expenses.
Why Minimum Credit Card Payments Take 30 Years — DTI Ratio, the Debt Spiral Condition, and Scenario Analysis
The minimum payment on a £5,000 credit card balance at 20% APR takes 28-32 years to repay and costs £7,500-9,000 in interest — more than the original debt. Here's the DTI calculation (with thresholds), the mathematical condition for a debt spiral (monthly interest ≥ monthly payments), how to use a loan planner to diagnose whether you're in slow-motion debt spiral territory, and the order-of-operations for debt vs saving decisions.
Why "40% Margin" Applied as a 40% Markup Produces Only 28.6% Gross Margin — And the Conversion Formula That Fixes It
Gross margin and markup describe the same profit relationship but calculate it differently — markup uses cost as the denominator, gross margin uses selling price. A business targeting "40% margin" that applies a 40% markup gets only 28.6% gross margin, systematically underpricing every product. Here's the conversion formula, why the two measures diverge dramatically at higher values (50% margin requires 100% markup), and the VAT extraction error that catches even mathematically confident people.
Senior Citizen FD Premiums, Tax-Saver Trade-Offs, and NRE vs NRO — How to Choose the Right Fixed Deposit
The 0.25-0.50% senior citizen FD premium isn't charity — it reflects banks competing for a high-balance, high-retention depositor segment. Here's why the Section 80C tax-saver FD sometimes loses to a regular FD at a higher rate once you account for the 5-year lock-in, how to correctly compare "special tenure" FDs at unusual maturities, and why NRE FDs have been particularly attractive for NRIs when Indian rates exceed foreign deposit rates.
Why Your Bank Extends the Loan Instead of Raising Your EMI — Variable Rate Mechanics and the Prepayment Decision
Floating rate loans that adjust tenure instead of EMI on a rate rise can extend your mortgage by 7+ years — costing ₹35+ lakh in additional payments — while keeping your monthly amount unchanged. Here's how the two rate-change adjustment mechanisms work (EMI adjustment vs tenure extension), why prepayment in the first year saves 3× more than the same amount in year 15, and India's RBI rules prohibiting prepayment charges on floating-rate home loans.
Why Legal Deadlines Are Harder to Calculate Than They Appear — Service Dates, Day Counting Rules, and Limitation Periods
Legal deadlines depend on whether "day 0" (the triggering event) is included or excluded from the count, which direction weekend/holiday adjustment goes, and when "service" is deemed to have occurred by method (first-class post adds 2 business days before the clock starts). Here's the CPR and US Federal Rules counting conventions, why posting a response on day 14 can still be late, and how limitation periods interact with the "date of knowledge" extension.
