Chapter 22: Financial Mathematics – Calculation of YTM (JAIIB – Paper 3)

1. Which of the following best defines 'Debt' in financial terms?

  • A. Ownership in a company
  • B. An obligation to repay borrowed funds with interest
  • C. A type of equity investment
  • D. A government grant
Debt represents borrowed money that must be repaid, usually with interest, distinguishing it from equity which represents ownership.

2. A bond is best described as:

  • A. A share of ownership in a company
  • B. A type of derivative contract
  • C. A short-term bank deposit
  • D. A debt instrument issued to raise funds with fixed interest
Bonds are debt instruments where the issuer promises to pay periodic interest and return principal at maturity.

3. Which term represents the stated annual interest rate of a bond?

  • A. Yield to Maturity (YTM)
  • B. Market price
  • C. Coupon rate
  • D. Face value
The coupon rate is the annual interest stated on the bond, expressed as a percentage of its face value.

4. The price of a bond is ₹9,500, its face value is ₹10,000, annual coupon is ₹800, and maturity is 5 years. What is the approximate Yield to Maturity (YTM)?

  • A. 9%
  • B. 8%
  • C. 10%
  • D. 11%
Approximate YTM = [Coupon + ((Face Value - Price)/Years)] / [(Face Value + Price)/2] = [800 + ((10,000-9,500)/5)] / [(10,000+9,500)/2] ≈ 9%

5. Face value of a bond refers to:

  • A. Market price at issuance
  • B. Nominal value to be repaid at maturity
  • C. Total coupon payment over life
  • D. Current trading price
The face value is the principal amount the issuer promises to repay at the bond’s maturity, also called par value.

6. Yield to Maturity (YTM) is best described as:

  • A. Annual coupon payment divided by market price
  • B. Difference between face value and market price
  • C. Total return expected if bond is held till maturity
  • D. Interest paid only in the first year
YTM represents the internal rate of return of the bond assuming it is held until maturity and all payments are made as scheduled.

7. If a bond’s market price is higher than its face value, it is said to be:

  • A. Discount bond
  • B. Zero-coupon bond
  • C. Callable bond
  • D. Premium bond
A premium bond is sold above its face value, usually because its coupon rate is higher than current market interest rates.

8. Which type of bond pays interest that adjusts periodically based on a reference rate like RBI’s repo rate?

  • A. Zero-coupon bond
  • B. Convertible bond
  • C. Floating rate bond
  • D. Premium bond
Floating rate bonds have variable interest payments tied to a benchmark rate, reducing interest rate risk.

9. A bond that can be repurchased by the issuer before maturity is called:

  • A. Zero-coupon bond
  • B. Callable bond
  • C. Convertible bond
  • D. Puttable bond
Callable bonds allow the issuer to redeem before maturity, often when interest rates fall, to reduce borrowing costs.

10. Which bond allows the holder to sell it back to the issuer at a pre-agreed price before maturity?

  • A. Puttable bond
  • B. Callable bond
  • C. Zero-coupon bond
  • D. Floating rate bond
Puttable bonds give the investor the right to sell back to the issuer, providing protection against rising interest rates.

11. A bond that can be converted into equity shares of the issuer is called:

  • A. Floating rate bond
  • B. Puttable bond
  • C. Callable bond
  • D. Convertible bond
Convertible bonds allow the holder to convert the bond into a fixed number of equity shares, combining debt and equity features.

12. The market price of a bond is calculated by:

  • A. Adding coupon rate to face value
  • B. Discounting all future cash flows to present value
  • C. Multiplying face value with coupon rate
  • D. Averaging the last 5 years’ prices
Bond valuation involves discounting all expected future cash flows (coupons and principal) at the required yield to calculate the present market price.

13. Which of the following will cause the price of a bond to rise?

  • A. Increase in market interest rates
  • B. Decrease in credit quality of issuer
  • C. Decrease in market interest rates
  • D. Increase in inflation
Bond prices and market interest rates move inversely; when rates fall, existing bonds with higher coupons become more valuable.

14. If a bond has a face value of ₹1,000, annual coupon of ₹100, maturity 5 years, and YTM of 10%, what is the approximate price?

  • A. ₹1,000
  • B. ₹950
  • C. ₹1,050
  • D. ₹1,100
When the coupon rate equals the YTM, the bond price equals face value. Here, coupon = 100/1000 = 10% = YTM, so price ≈ ₹1,000.

15. Which term refers to the sensitivity of a bond’s price to changes in interest rates?

  • A. Coupon rate
  • B. Face value
  • C. YTM
  • D. Duration
Duration measures the weighted average time to receive a bond’s cash flows and indicates price sensitivity to interest rate changes.

16. A bond has a face value of ₹10,000, annual coupon of 12%, and pays interest semi-annually. What is the semi-annual coupon payment?

  • A. ₹600
  • B. ₹1,200
  • C. ₹6000
  • D. ₹12,000
Annual coupon = 12% of ₹10,000 = ₹1,200; Semi-annual payment = ₹1,200 ÷ 2 = ₹600.

17. When a bond pays interest semi-annually, the formula for its present value is adjusted by:

  • A. Doubling the YTM and halving the number of periods
  • B. Halving the YTM and doubling the number of periods
  • C. Using annual YTM without adjustment
  • D. Ignoring coupon payments
For semi-annual bonds, YTM is divided by 2 and the number of periods is doubled when discounting cash flows.

18. Current yield of a bond is defined as:

  • A. Annual coupon payment divided by current market price
  • B. Face value divided by market price
  • C. YTM minus coupon rate
  • D. Total cash flow divided by years to maturity
Current yield = Annual coupon / Market price; it measures the income component of return relative to the bond’s price.

19. A bond has a face value of ₹5,000, annual coupon of ₹400, and current market price ₹4,800. What is the current yield?

  • A. 7%
  • B. 8%
  • C. 8.33%
  • D. 9%
Current yield = Annual coupon ÷ Market price = 400 ÷ 4,800 ≈ 8.33%.

20. If the market price of a bond rises above its face value, the current yield will:

  • A. Increase
  • B. Remain the same
  • C. Equal the coupon rate
  • D. Decrease
Current yield = Coupon ÷ Market price; as price rises, the denominator increases, so the yield decreases.

21. Semi-annual bond pricing requires how many discounting periods if the bond matures in 6 years?

  • A. 6 periods
  • B. 12 periods
  • C. 3 periods
  • D. 24 periods
Semi-annual payments double the number of periods: 6 years × 2 = 12 periods.

22. Which of the following statements is true regarding current yield?

  • A. It considers capital gains or losses
  • B. It is the same as YTM
  • C. It measures only the income component of return
  • D. It is always higher than coupon rate
Current yield ignores capital gains/losses and focuses only on the annual coupon relative to market price.

23. If a semi-annual bond’s YTM is 8% per annum, what is the per period discount rate?

  • A. 4%
  • B. 8%
  • C. 16%
  • D. 2%
For semi-annual bonds, per period rate = annual YTM ÷ 2 = 8% ÷ 2 = 4%.

24. A bond’s price and its current yield move in which relation?

  • A. Directly proportional
  • B. Inversely proportional
  • C. No relation
  • D. Equal only for zero-coupon bonds
As bond price rises, current yield = coupon ÷ price decreases; hence, they move inversely.

25. Which formula is used to calculate the price of a bond with semi-annual interest payments?

  • A. Price = Face value + Coupon
  • B. Price = Coupon ÷ YTM
  • C. Price = Face value ÷ (1 + YTM)^n
  • D. Price = Σ (Coupon/2 ÷ (1 + YTM/2)^t) + (Face value ÷ (1 + YTM/2)^(2n))
Semi-annual bond price = sum of discounted semi-annual coupon payments + discounted face value, adjusting YTM and periods for semi-annual compounding.

26. Yield-to-Maturity (YTM) of a bond is best described as:

  • A. Coupon rate divided by face value
  • B. The internal rate of return if the bond is held till maturity
  • C. Current yield minus capital gains
  • D. Annual interest received divided by purchase price
YTM is the discount rate that equates the present value of all future cash flows (coupons and principal) to the current market price of the bond.

27. Which theorem states that the price of a bond is inversely related to changes in market interest rates?

  • A. Fisher’s theorem
  • B. Modigliani-Miller theorem
  • C. Bond pricing theorem
  • D. Efficient market hypothesis
The bond pricing theorem highlights that bond prices move inversely with market interest rates due to fixed coupon payments.

28. A bond with face value ₹1,000, price ₹950, annual coupon ₹100, and 3 years to maturity has a YTM approximately equal to:

  • A. 11.6%
  • B. 10%
  • C. 12%
  • D. 9%
Approximate YTM = [Coupon + ((Face value - Price)/Years)] / [(Face value + Price)/2] = [100 + (50/3)] / [(1,000+950)/2] ≈ 11.6%

29. According to the theorem of bond value, a bond selling at a premium will have:

  • A. YTM equal to coupon rate
  • B. Current yield less than coupon rate
  • C. Face value greater than market price
  • D. YTM less than coupon rate
For a premium bond, price > face value, so the yield-to-maturity is lower than the coupon rate.

30. In bond valuation illustrations, which factor does NOT affect the bond’s present value?

  • A. Coupon rate
  • B. Maturity period
  • C. Issuer’s logo
  • D. Required yield/YTM
The issuer’s logo does not affect the bond’s valuation; only cash flows, coupon rate, maturity, and required yield matter.

31. Which of the following illustrates the effect of time to maturity on bond price?

  • A. Longer maturity always increases bond price
  • B. Longer maturity increases price volatility for a given change in interest rates
  • C. Time to maturity has no effect
  • D. Bond price decreases linearly with maturity
Longer maturity increases a bond’s sensitivity to interest rate changes, making prices more volatile.

32. For a zero-coupon bond, the YTM can be calculated using:

  • A. Current yield formula
  • B. Coupon rate formula
  • C. Price × Coupon rate
  • D. (Face value / Price)^(1/n) - 1
Zero-coupon bonds do not pay periodic coupons; YTM is calculated as the compound rate equating price to face value: YTM = (FV/Price)^(1/n) - 1.

33. If market interest rates fall, illustrations show that the price of a bond will:

  • A. Remain constant
  • B. Decrease slightly
  • C. Increase
  • D. Become negative
Bond prices move inversely with market interest rates; when rates fall, existing bonds with higher coupons increase in value.

34. In bond illustrations, the price of a bond with a higher coupon rate compared to market YTM will:

  • A. Equal face value
  • B. Sell at a premium
  • C. Sell at a discount
  • D. Be unaffected by market rates
When the bond’s coupon rate > market YTM, its price is higher than face value (premium bond) to match yield expectations.

35. Which factor increases the Yield-to-Maturity for a bond purchased at a discount?

  • A. Market price below face value
  • B. High coupon rate
  • C. Long maturity with premium price
  • D. Semi-annual payments
YTM rises when a bond is purchased below face value because total return includes both coupon payments and capital gain at maturity.

36. What does the duration of a bond measure?

  • A. Time until the next coupon payment
  • B. Weighted average time to receive all cash flows
  • C. Number of years to maturity only
  • D. Total coupon payments
Duration measures the weighted average time in years to receive the bond’s cash flows, indicating interest rate sensitivity.

37. Which of the following statements about bond duration is true?

  • A. Higher coupon increases duration
  • B. Longer maturity decreases duration
  • C. Duration decreases as coupon rate increases
  • D. Duration is independent of yield
Higher coupons lead to earlier cash flows, reducing weighted average time; hence duration decreases as coupon rate increases.

38. Modified duration is used to estimate:

  • A. Percentage change in bond price for a 1% change in yield
  • B. Total coupon payments
  • C. Time to next coupon
  • D. Yield-to-maturity
Modified duration adjusts Macaulay duration for yield to measure bond price sensitivity to interest rate changes.

39. Which property of duration is correct?

  • A. Duration increases with higher coupon rates
  • B. Duration increases with longer time to maturity
  • C. Duration decreases with lower maturity
  • D. Duration is unaffected by yield
Duration increases with longer time to maturity because cash flows are received later, making bond price more sensitive to interest rate changes.

40. Which of the following is true regarding bond price volatility?

  • A. High coupon bonds are more volatile than low coupon bonds
  • B. Short-term bonds are more volatile than long-term bonds
  • C. Low coupon, long-term bonds are most volatile
  • D. Volatility is independent of coupon and maturity
Low coupon and long-term bonds have longer duration, making them more sensitive to interest rate changes, hence more volatile.

41. A 5-year bond with duration of 4 years and modified duration of 3.8 estimates that a 1% increase in yield will cause approximate price change of:

  • A. +3.8%
  • B. -3.8%
  • C. -4%
  • D. +4%
Modified duration indicates approximate percentage price change: ΔP/P ≈ -Modified Duration × ΔYield = -3.8 × 1% = -3.8%.

42. Which factor reduces bond price volatility?

  • A. Longer maturity
  • B. Lower coupon rate
  • C. High market yield
  • D. Higher coupon rate
Higher coupon bonds return cash flows earlier, reducing weighted duration and making them less sensitive to interest rate changes.

43. Macaulay duration is measured in:

  • A. Percentage
  • B. Years
  • C. Currency units
  • D. Basis points
Macaulay duration is expressed in years as the weighted average time to receive the bond’s cash flows.

44. Which type of bond will have the lowest duration?

  • A. Long-term, low coupon
  • B. Long-term, high coupon
  • C. Short-term, high coupon
  • D. Short-term, zero coupon
Short-term high coupon bonds return cash flows quickly, reducing duration and price sensitivity to interest rates.

45. When solving bond duration problems, which approach is commonly used?

  • A. Ignoring cash flows and focusing on maturity
  • B. Weighted average of present value of cash flows divided by bond price
  • C. Summing coupons only
  • D. Using only YTM without cash flows
Duration = Σ (t × PV of cash flow) / Price; this weighted average approach is standard for duration calculations.

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