A 21-year German government bond (bund) has a face value of €550 and a coupon rate of 4% paid annually. Assume that the interest rate (in euros) is equal to 7.10% per year. What is the bond's PV? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Question

BlackTom AI · Accepted Answer

PV = PV(coupon annuity) + PV(face value). Relevant concepts: coupon payment C = coupon rate × face value; discounting uses r per period and n periods; PV of an n‑period annuity = C × [1 − (1+r)^−n]/r; PV of principal = FV × (1+r)^−n.

Given: FV = €550, coupon rate = 4% → C = 0.04×550 = €22 per year; r = 7.10% = 0.071; n = 21.

Step-by-step computation:
1) Compute (1+r)^21:
   (1.071)^21 ≈ 4.222589756067144 (intermediate calculation shown above by iterative multiplication).
2) Compute discount factor for year 21:
   v^21 = (1.071)^−21 = 1 / 4.222589756067144 ≈ 0.236817999.
3) PV of coupon annuity:
   annuity factor = [1 − v^21] / r = [1 − 0.236817999] / 0.071
                   = 0.763182001 / 0.071 ≈ 10.749028169.
   PV(coupons) = C × annuity factor = 22 × 10.749028169 ≈ €236.4786197.
4) PV of face value:
   PV(FV) = 550 × v^21 = 550 × 0.236817999 ≈ €130.2498995.
5) Total PV:
   PV = 236.4786197 + 130.2498995 = €366.7285192.
   Rounded to two decimals: €366.73.

Why this option is correct: the calculation uses the correct coupon (€22), correct discount rate (7.10%), and discounts both coupon stream and principal for 21 years. The final rounded PV €366.73 matches option b.

Why other options are incorrect:
- a. €266.73 is far too low (would require much lower annuity or incorrectly using a much higher discount rate or miscomputing coupon).
- c. €365.73 differs by €1.00 likely from a small arithmetic/rounding error; it does not match the exact PV.
- d. €376.73 is about €10 too high (would result from under-discounting or using a lower interest rate).

Confirming final answer: b. 366.73.

A 21-year German government bond (bund) has a face value of €550 and a coupon rate of 4% paid annually. Assume that the interest rate (in euros) is equal to 7.10% per year. What is the bond's PV? (Do not round intermediate calculations. Round your answer to 2 decimal places.)单项选择题

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