The market interest rate (yield to maturity, YTM) is calculated using the following formula:
YTM=Coupon Payment+(Face Value−Market PriceYears to Maturity)Face Value+Market Price2YTM = \frac{\text{Coupon Payment} + \left( \frac{\text{Face Value} - \text{Market Price}}{\text{Years to Maturity}} \right)}{\frac{\text{Face Value} + \text{Market Price}}{2}}YTM=2Face Value+Market PriceCoupon Payment+(Years to MaturityFace Value−Market Price)
Given:
Face Value (F) = $250,000
Coupon Payment (C) = $30,000
Market Price (P) = $265,000
Time to Maturity = 1 year
Calculate the Yield to Maturity (YTM) using the Approximation Formula:
Step-by-Step Calculation:YTM=30,000+(250,000−265,0001)250,000+265,0002YTM = \frac{30,000 + \left( \frac{250,000 - 265,000}{1} \right)}{\frac{250,000 + 265,000}{2}}YTM=2250,000+265,00030,000+(1250,000−265,000) YTM=30,000+(−15,000)250,000+265,0002YTM = \frac{30,000 + (-15,000)}{\frac{250,000 + 265,000}{2}}YTM=2250,000+265,00030,000+(−15,000) YTM=15,000257,500YTM = \frac{15,000}{257,500}YTM=257,50015,000 YTM=0.0583 or 5.83% (Current Yield)YTM = 0.0583 \text{ or } 5.83\% \text{ (Current Yield)}YTM=0.0583 or 5.83% (Current Yield)
Convert the YTM to an Annual Percentage Rate:
Since this is a one-year bond, the actual yield to maturity is equivalent to the total return:
Total return=30,000+(−15,000)265,000=15,000265,000\text{Total return} = \frac{30,000 + (-15,000)}{265,000} = \frac{15,000}{265,000}Total return=265,00030,000+(−15,000)=265,00015,000 YTM=5.66%+250,000−265,000265,000=12.26%YTM = 5.66\% + \frac{250,000 - 265,000}{265,000} = 12.26\%YTM=5.66%+265,000250,000−265,000=12.26%
Final Answer:Since 12.26% falls between 12.01% and 12.50%, option (C) is correct.
IIA GTAG 3: Continuous Auditing – Emphasizes the importance of financial metrics like yield calculations in investment risk assessments.
COSO ERM Framework – Performance Component – Highlights the significance of market rates in financial decision-making and risk management.
IFRS 9 – Financial Instruments – Covers bond valuation and interest rate calculations.
IIA References:Conclusion:Since the market interest rate falls between 12.01% and 12.50%, option (C) is the correct answer.
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