Time Value of Money — Formulas, Annuities, EMI
Everything money-related compounds. If you nail PV / FV / annuity formulas, you'll cover 5–7 marks every attempt — and Intermediate FM becomes trivial.
Last reviewed: 25 April 2026
Core intuition
- •₹1 today > ₹1 next year because today's rupee can earn interest.
- •Discounting: bring a future amount to today's value.
- •Compounding: push today's amount to a future value.
Simple vs Compound Interest
- •Simple interest: interest each period is based on the original principal only.
- •Compound interest: interest each period includes interest on previously-earned interest.
- •At any rate > 0 and time > 1 period, CI > SI.
Annuities
- •Ordinary annuity: equal payments at the END of each period (most common in exams).
- •Annuity due: equal payments at the BEGINNING of each period. Multiply ordinary annuity value by (1 + r) to convert.
- •Perpetuity: annuity that continues forever. PV = PMT / r.
EMI (Equated Monthly Instalment)
- •Each EMI covers part interest + part principal.
- •Interest component is highest in the first EMI and falls each month as principal outstanding shrinks.
- •Use monthly rate (annual rate ÷ 12) and months (years × 12) when applying the formula.
Formulas
- Future value (compound)
- FV = PV × (1 + r)^n
- Present value
- PV = FV ÷ (1 + r)^n
- Ordinary annuity — FV
- FV = PMT × [((1 + r)^n − 1) / r]
- Ordinary annuity — PV
- PV = PMT × [1 − (1 + r)^−n] / r
- Annuity due — PV/FV
- Multiply the ordinary-annuity value by (1 + r).
- Perpetuity — PV
- PV = PMT / r
- EMI
- EMI = P × r × (1 + r)^n / ((1 + r)^n − 1)
r = monthly rate (annual% ÷ 12 ÷ 100), n = number of months.
Must know before the exam
- ★Always match the period of rate and n. Annual rate with monthly payments → convert rate to monthly FIRST.
- ★An annuity-due can be thought of as an ordinary annuity shifted one period earlier.
- ★Rule of 72: time to double ≈ 72 / rate%. At 9%, ~8 years.
- ★EMI's first month is mostly interest; for long-tenure loans, it flips to mostly principal near the end.
Common mistakes & fixes
- ✗ Applying annual rate with monthly n in the EMI formula.
- ✓ Convert annual rate to monthly (÷ 12) AND time to months (× 12). Both must match.
- ✗ Confusing annuity due and ordinary annuity.
- ✓ Read the problem: 'beginning of each year' = due; 'end of each year' = ordinary.
Lock it in with practice
Reading without practising is the #1 reason people forget in the exam. Solve a quick set while this is fresh.