Chapter 22: Financial Mathematics — Calculation of YTM

📚 JAIIB 2026 • AFM • Module C • Chapter 4 of 10 • Unit 22

Financial Mathematics — Calculation of YTM
(Bonds — Valuation, Yield & Duration!)

Banks hold crores in bonds. Understanding bond valuation, YTM, current yield, and duration is critical for treasury and the JAIIB exam. This chapter covers all bond mathematics.

⏱ 24 min read🎯 Treasury Critical⚡ 12 Flash Cards

Banky Enters the Bond Market! 📊💰

The bank holds ₹500 crore in bonds. When rates rise, prices FALL — crores lost! Banky needs to understand WHY and HOW.

“Sir, rates went up 1% and treasury showed ₹10 crore loss! But we haven’t SOLD them!” 😱 — “That’s mark-to-market. Bond prices are INVERSE to rates!” 📉
🚀
Section 1 of 9

Bonds — Everything You Need

📖 Part 1 — What is a Bond? Key Terms + Types

Bond = Debt instrument. Issuer pays fixed interest (coupon) periodically + returns principal at maturity. Bonds are NOT part of net worth — they are DEBT! Interest is TAX DEDUCTIBLE (tax shield).

6 Terms: Face/Par Value (₹100/₹1,000), Coupon Rate (fixed %), Maturity (when returned), Redemption Value (amount at maturity), Market Value (trading price), Day Count (Actual/365, 30/360 etc.).

Types: Fixed rate, Floating (FRN), Zero-coupon (no interest, issued at discount), Junk/High-yield (below investment grade), Convertible (exchange for equity), Inflation-indexed, Perpetual (no maturity), Govt/Treasury (risk-free), Callable (issuer repays early), Putable (holder forces early repayment), Bearer (no named holder).

🧑‍💼 Banky: “Bond = I lend money, they pay me interest, and return my money at the end. Bonds are DEBT, not equity!” 📋

📊 Part 2 — Bond Valuation + 3 Key Rules

Bond Value = I × PVIFA(kd,n) + F × PVIF(kd,n)

I = coupon, F = face value, kd = required return, n = years. Example: ₹1,000 par, 12% coupon, 3 yrs, 10% required → 120(2.487) + 1,000(0.751) = ₹1,049 → PREMIUM (coupon > market rate).

Semi-annual: Coupon ÷ 2, kd ÷ 2, n × 2. Value slightly higher (reinvestment advantage).

3 Rules: (1) Coupon > Market → PREMIUM. (2) Coupon < Market → DISCOUNT. (3) Coupon = Market → PAR VALUE.

🧑‍💼 Banky: “Price and rate = SEESAW ⚖️! Rate UP → Price DOWN. Rate DOWN → Price UP!” 📉📈

💰 Part 3 — Current Yield, YTM, Duration

Current Yield = Coupon ÷ Market Price (simple, ignores capital gain/loss)
YTM = Discount rate where PV of all cash flows = Market Price (total return if held to maturity)

YTM includes coupon + capital gain/loss. Found by trial & error. At discount → YTM > coupon. At premium → YTM < coupon. At par → YTM = coupon.

Duration = Weighted average time of all cash flows = Holding period where rate risk vanishes

Properties: Duration ≤ maturity. Zero-coupon: Duration = Maturity. Higher coupon → shorter duration. Longer maturity → longer duration. Higher YTM → shorter duration.

🧑‍💼 Banky: “Current Yield = TODAY. YTM = TOTAL if held. Duration = MAGIC point where risk vanishes!” 🎯
🎯
Section 2 of 9

Exam-Ready Points

🎯 Must Remember!

  • Bond = DEBT, NOT net worth! Interest is tax-deductible. “Bonds are part of net worth” = WRONG!
  • Coupon > Market → Premium. Coupon < Market → Discount. Equal → Par.
  • Price ↔ Rate: INVERSE. Rate ↑ = Price ↓.
  • Current Yield = Coupon ÷ Price. Simple. Ignores capital gain/loss.
  • YTM = Total return held to maturity. Most complete measure.
  • Duration = Holding period where interest rate risk disappears.
  • Zero-coupon: Duration = Maturity exactly. No periodic interest. Issued at discount.
  • Higher coupon → shorter duration. Longer maturity → longer duration.
  • Callable + Putable: Bonds can have BOTH options!
  • Perpetual bond value = Coupon ÷ Required Return.

📝 Past Exam Questions

Q: Which about bonds is NOT correct?
A: “Bonds are part of net worth” — WRONG! They are DEBT.
Q: Duration of a bond is?
A: Holding period for which interest rate risk disappears.
Q: When required rate = coupon rate, bond value?
A: Equal to par value.
Q: Bonds can be issued with?
A: Both put AND call option.
Q: Zero-coupon bonds?
A: All correct — no regular interest, issued at discount, full principal at redemption.
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Section 3 of 9

Last-Minute Flash Cards

Bond = Debt
NOT net worth! Bondholder = CREDITOR
Interest tax-deductible. Dividends NOT.
Bond Value
= I×PVIFA + F×PVIF
PV of coupons + PV of redemption.
Price vs Rate
INVERSE seesaw ⚖️
Rate↑=Price↓. Coupon>Market=Premium. Equal=Par.
Current Yield
= Coupon ÷ Market Price
Simple. Ignores capital gain/loss.
YTM
Total return if held to maturity
Includes coupon + capital gain. Trial & error.
Duration
Holding period where rate risk vanishes
Zero-coupon: Duration=Maturity. Always ≤ maturity.
Duration Properties
↑Coupon=↓Duration | ↑Maturity=↑Duration
Higher YTM → shorter duration.
Zero-Coupon
No interest | Discount issue | Par redemption
Duration = Maturity exactly.
Call vs Put
Call=issuer repays early | Put=holder forces early
Bonds can have BOTH!
Perpetual Bond
Value = Coupon ÷ Required Return
No maturity. Pays forever.
Junk Bonds
Below investment grade | HIGH yield
Higher risk = higher return.
Semi-Annual
Coupon÷2, Rate÷2, n×2
Slightly higher value than annual.

⚡ Module C • Chapter 4 (Unit 22) Done!

  • Bond = DEBT, NOT net worth. Interest tax-deductible. Bondholder = creditor.
  • Value: I×PVIFA + F×PVIF. Coupon>Market→Premium. Equal→Par. Coupon
  • Price ↔ Rate: INVERSE seesaw. Rate↑ → Price↓.
  • Current Yield: Coupon÷Price (simple). YTM: Total return to maturity (complete).
  • Duration: Rate risk vanishes. Zero-coupon=Maturity. ≤Maturity always.
  • Types: Fixed, Float, Zero, Junk, Convert, Call, Put, Perpetual, Govt, Bearer.

Banky says: “Bonds=debt! Price↔Rate=seesaw! YTM=total return! Duration=magic point! Now I understand treasury!” 🎉📊

Next: Chapter 23 — Forex Arithmetic! 💪🌍

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