Chapter 21: Financial Mathematics — Interest & Annuities

📚 JAIIB 2026 • AFM • Module C • Chapter 3 of 10 • Unit 21

Financial Mathematics — Interest & Annuities
(The Math Behind Every Loan, Deposit, EMI & Investment!)

Every banker calculates interest daily. SI for short-term. CI for deposits. EMI for home loans. This chapter covers ALL the math — SI, CI, Rule of 72, Fixed vs Floating, Front-end vs Back-end, Ordinary Annuity, Annuity Due, EMI formula, and Sinking Funds.

⏱ 26 min read🎯 Calculation Heavy🧠 8 Memory Tricks⚡ 14 Flash Cards

Banky Does the MATH! 🧮📐

A customer asks: “What’s my EMI for a ₹10 lakh home loan at 10.5% for 15 years?” Banky needs the FORMULA!

“Sir, how do I calculate EMI? What’s the difference between SI and CI? What’s an Annuity?” 🤔
🚀
Section 1 of 9

All Formulas — Simple to Advanced

📖 Part 1 — Simple Interest vs Compound Interest

Simple Interest = P × r × t  |  Amount = P(1 + rt)

P = Principal, r = rate (decimal), t = time (years). Interest on ORIGINAL principal only.

Example: ₹60,000 at 12% for 2 years → SI = 60,000 × 0.12 × 2 = ₹14,400. ₹40,000 at 11% for 3 years → SI = ₹13,200 (exam question!)

Compound Interest: A = P(1 + r/n)nt

n = compounding frequency. Annual: n=1. Quarterly: n=4. Monthly: n=12. MORE frequent = MORE interest. CI always ≥ SI.

Rule of 72: Money DOUBLES in 72 ÷ rate years. At 6% → 12 yrs. At 8% → 9 yrs. At 12% → 6 yrs.

Depreciation: BV = Original × (1 − rate)n. ₹20,000, 10%, 3 yrs → ₹14,580.

🧑‍💼 Banky: “SI = flat rent. CI = snowball rolling downhill! Rule of 72 = magic shortcut!” ❄️

📋 Part 2 — Fixed vs Floating, Front-end vs Back-end

Fixed: Rate stays same for entire tenure. Usually HIGHER. No market risk. Floating: Changes with benchmark (MCLR). Usually LOWER initially.

Front-end: Interest deducted UPFRONT (bill discounting). Effective rate HIGHER. Back-end: Full amount disbursed. Interest charged later. Normal for term loans.

Product method (CC/OD/SB): Daily balance × days = product. Sum × rate ÷ 365 = interest.

🧑‍💼 Banky: “Fixed = locked 🔒. Floating = rollercoaster 🎢. Front-end = you get less money!” 📊

💰 Part 3 — Annuities: Ordinary vs Due

Annuity = Series of FIXED payments at REGULAR intervals. EMI, RD, rent = annuities.

Ordinary: Payment at END (salary). Due: Payment at BEGINNING (rent). Due > Ordinary by factor (1+i).

FV (Ordinary) = C × [(1+i)n − 1] / i
PV (Ordinary) = C × [(1+r)n − 1] / [r(1+r)n]
Due = Ordinary × (1 + i) — for both FV and PV

“Special Annuity” is NOT a real type! Only Ordinary and Due exist.

🏦 Part 4 — EMI + Sinking Fund

EMI = P × r × (1+r)n / [(1+r)n − 1]

P = loan, r = monthly rate, n = total instalments. First EMIs = MORE interest. Later = MORE principal.

3 Repayment Methods: (1) Equal principal + declining interest. (2) EMI (equal total). (3) Bullet/balloon (all at end).

Sinking Fund: Equal periodic deposits to accumulate target amount. Used for equipment replacement, bullet loan repayment.

🧑‍💼 Banky: “EMI = most used formula in retail banking! First EMIs heavy on interest, later heavy on principal!” 🍰
🎯
Section 2 of 9

Exam-Ready Points

🎯 Must Remember!

  • SI = P×r×t. CI: A = P(1+r/n)nt. CI ≥ SI always.
  • Rule of 72: Doubling time = 72 ÷ rate.
  • More frequent compounding = MORE total interest (monthly > quarterly > annual).
  • Fixed rate: Stays same, usually HIGHER. Floating: Changes with MCLR, usually LOWER initially.
  • Front-end: Interest upfront, effective rate HIGHER. Back-end: Full disbursement, interest later.
  • “Special Annuity” is NOT a type! Only Ordinary (end) and Due (beginning).
  • Due values > Ordinary by (1+i) factor.
  • EMI = P×r×(1+r)n/[(1+r)n−1]. Interest-heavy at start, principal-heavy at end.
  • Sinking Fund: When specified amount needed at specified future date.
  • ₹40,000 at 11% SI for 3 years = ₹13,200.
  • All compounding statements correct: Shorter period = more interest, CI on P+accumulated, CI > SI.

📝 Past Exam Questions

Q: ₹40,000 at 11% SI for 3 years = ?
A: ₹13,200
Q: Which is NOT a type of Annuity?
A: “Special Annuity” — NOT real! Only Ordinary and Due.
Q: Compounding statements?
A: ALL correct — shorter period = more, CI on P+I, CI > SI.
Q: Sinking fund is created?
A: When specified amount needed at specified future date.
Q: Repayment methods?
A: All — Equal principal, EMI, Bullet/balloon.
⚡
Section 3 of 9

Last-Minute Flash Cards

Simple Interest
SI = P × r × t
Interest on PRINCIPAL only. Flat. Short-term.
Compound Interest
A = P(1 + r/n)nt
Interest on principal + accumulated. Snowball! CI ≥ SI.
Rule of 72
Years to double = 72 ÷ rate
6%→12yrs | 8%→9yrs | 12%→6yrs
Fixed vs Floating
Fixed = locked 🔒 | Floating = market-linked 🎢
Fixed usually HIGHER. Floating linked to MCLR.
Front-end vs Back-end
Front = deducted upfront (effective rate HIGHER)
Back-end = full disbursement, interest later. Normal practice.
Ordinary vs Due
Ordinary = END | Due = BEGINNING
Due > Ordinary by (1+i). “Special” = NOT a type!
EMI Formula
EMI = P×r×(1+r)n/[(1+r)n−1]
Interest-heavy start, principal-heavy end. Excel: =PMT().
Sinking Fund
Periodic deposits for future target amount
Equipment replacement, bullet loan repayment. F=A×[(1+i)n−1]/i.
3 Repayment Methods
Equal principal | EMI | Bullet/Balloon
EMI most common in retail banking.
Continuous Compounding
A = Pert (n → ∞)
e ≈ 2.71828. Maximum possible interest.

⚡ Module C • Chapter 3 (Unit 21) Done!

  • SI = P×r×t (flat). CI = P(1+r/n)nt (snowball). Rule of 72 = 72÷rate.
  • Fixed: Same rate (higher). Floating: Market-linked (lower initially). Front-end = upfront deduction.
  • Ordinary: End. Due: Beginning. Due > Ordinary by (1+i). “Special” = NOT a type!
  • EMI = P×r×(1+r)n/[(1+r)n−1]. Interest-heavy start. 3 methods: Equal P, EMI, Bullet.
  • Sinking Fund: Periodic deposits for target amount. For equipment/bullet loans.

Banky says: “SI = flat, CI = snowball! Rule of 72! EMI = most used formula! Ordinary = END, Due = BEGINNING! Now I can calculate ANYTHING!” 🎉🧮

Next: Chapter 22 — Financial Mathematics: YTM (Bonds!) 💪

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