The path to acing the FINRA Series 7 exam starts with a deep understanding of critical topics like accrued interest. This article provides you with practical examples, questions, and detailed explanations to solidify your understanding of this essential concept in corporate and government bond investments.
Understanding Accrued Interest
Accrued interest is the interest that accumulates on a bond between its previous interest payment and the transaction’s settlement date. This is a crucial topic for anyone dealing with fixed-income securities, as understanding it is paramount in evaluating bond pricing accurately.
Why is Accrued Interest Important?
- Financial Accuracy: Ensures accurate calculations in bond transactions.
- Investor Equity: Guarantees that the seller is compensated for the time they held the bond before sale.
- Pricing Bonds: Integral in calculating the full or “dirty” price of a bond.
Components of Accrued Interest Calculation
- Coupon Rate: The annual interest percentage payable.
- Par Value: The face value of the bond.
- Days of Interest Accumulation: Time from the last payment date to the settlement date.
$$
AI = \left(\frac{{\text{Coupon Rate} \times \text{Par Value}}}{\text{Annual Payment Frequency}}\right) \times \left(\frac{\text{Days Since Last Payment}}{\text{Days in Year}}\right)
$$
Note: Commonly, 360 days are used for corporate and municipal bonds, while treasury securities typically use a 365-day year.
Practice Problems and Detailed Answers
Let’s solidify your understanding with practice questions that simulate real-world scenarios. Explore intricate details and explanations to ensure you’re exam-ready.
### A bond with a 6% coupon rate and $1,000 face value pays interest semi-annually. If 90 days have passed since the last payment, calculate the accrued interest.
- [x] $15.00
- [ ] $30.00
- [ ] $18.00
- [ ] $10.00
> **Explanation:** First, calculate the semi-annual interest: $(0.06 \times 1000) / 2 = 30$. Then, compute the accrued interest: $(30 \times 90) / 180 = 15$.
### Calculate the accrued interest for a municipal bond with a 7% annual coupon rate, a $5,000 par value, with 60 days since last interest payment and operating on a 360-day year.
- [x] $58.33
- [ ] $70.00
- [x] $58.33
- [ ] $33.33
> **Explanation:** Semi-annual interest = $(0.07 \times 5000) / 2 = 175$. Accrued interest: $(175 \times 60) / 180 = 58.33$.
### You purchase a bond 75 days after its last interest payment. The bond has a coupon rate of 5.5% and a par value of $2,000. Calculate the accrued interest.
- [x] $22.92
- [ ] $20.42
- [ ] $25.50
- [ ] $27.78
> **Explanation:** Semi-annual interest: $(0.055 \times 2000) / 2 = 55$. Accrued Interest: $(55 \times 75) / 180 = 22.92$.
### For an investor buying a bond 45 days after the last interest payment, what is the accrued interest on a $3,000 bond with a 4% coupon rate, given a 360-day year?
- [x] $15.00
- [ ] $12.00
- [ ] $18.00
- [ ] $20.00
> **Explanation:** Semi-annual interest: $(0.04 \times 3000) / 2 = 60$. Accrued Interest: $(60 \times 45) / 180 = 15.00$.
### Determine the accrued interest for a treasury bond with a 3.5% annual coupon on a $10,000 face value, purchased 120 days after the last interest payment on a 365-day year.
- [x] $115.07
- [ ] $120.00
- [x] $115.07
- [ ] $85.00
> **Explanation:** Semi-annual interest: $(0.035 \times 10000) / 2 = 175$. Accrued interest: $(175 \times 120) / 365 = 115.07$.
### What is the accrued interest for a corporate bond with an 8% annual coupon rate, $2,500 par value, after 132 days of accumulation?
- [x] $73.33
- [ ] $88.89
- [ ] $66.67
- [ ] $100.00
> **Explanation:** Semi-annual interest: $(0.08 \times 2500) / 2 = 100$. Accrued interest: $(100 \times 132) / 180 = 73.33$.
### Compute the accrued interest for a $1,500 bond with a 9.5% coupon rate, 45 days post last semi-annual payment.
- [x] $17.81
- [ ] $15.63
- [x] $17.81
- [ ] $20.63
> **Explanation:** Semi-annual interest: $(0.095 \times 1500) / 2 = 71.25$. Accrued interest: $(71.25 \times 45) / 180 = 17.8125$.
### A $5,000 bond with a 6.25% coupon rate accumulates interest for 150 days. Calculate the accrued interest assuming a 360-day year.
- [x] $130.21
- [ ] $125.00
- [ ] $145.83
- [ ] $150.00
> **Explanation:** Semi-annual interest: $(0.0625 \times 5000) / 2 = 156.25$. Accrued interest: $(156.25 \times 150) / 180 = 130.21$.
### Determine accrued interest for a $4,000 bond, 8% coupon rate, with 180 days since the last payment.
- [x] $160.00
- [ ] $320.00
- [ ] $130.00
- [ ] $180.00
> **Explanation:** Semi-annual interest remains the same as the interest period is complete. Accrued interest: $160$.
### True or False: Accrued interest is only applicable to bonds with annual coupon payments.
- [x] False
- [ ] True
> **Explanation:** Accrued interest applies to all bonds regardless of whether they have annual, semi-annual, or quarterly coupon payments.
- Coupon Rate: The yield paid by the bond on its face value.
- Par Value: The nominal or face value of a bond or stock.
- Dirty Price: The total price of a bond that includes accrued interest.
- Settlement Date: The date on which payment is made to finalize the transaction.
Additional Resources
Final Summary
Mastering the calculation of accrued interest is crucial for those pursuing a career in securities as a representative. Proper comprehension ensures fairness in transactions and accuracy in bond pricing. By working through these representative questions and utilizing resource materials, candidates can better prepare for the Series 7 exam and succeed in the financial industry.