Final answer:
The price of a risk-free bond is calculated using the present value formula, which accounts for discounted future cash flows. However, without the specific spot rates of interest, the exact price calculation is impossible. Generally, bond prices decrease when interest rates rise, demonstrating the inverse relationship between bonds and interest rates.
Step-by-step explanation:
The question deals with the calculation of the price of a risk-free bond with specific cash flows. The bond in question pays $100 annual coupons, has a face value of $1,000, and matures in 4 years. To find the price of the bond, we need to calculate the present value of its future cash flows, including the annual coupons and the face value repayment at maturity, discounted at the spot rate of interest for each respective year. This is known as the present value formula for bonds. The spot rates for each of the relevant years to maturity are necessary to accurately calculate this price, but they are not provided in the question. In a hypothetical situation with certain interest rate changes, we can further see that bond prices are inversely related to interest rates.
For example, using generic interest rates, the price of the bond could be calculated as the sum of the present values of all the annual coupon payments and the face value. If we assume an 8% interest rate, the present value of a single $100 coupon would be calculated as $100 / (1 + 0.08), and similarly for the other cash flows, taking into account that each cash flow must be discounted for as many years as it is away from the present.
If, however, the interest rates rise to 12%, then the price is recalculated using the new interest rate, which would lead to a lower price due to a higher discount rate, making the bond less attractive if it pays a lower rate than the prevailing market rate. In both cases, you discount future cash flows back to their present value at the respective interest rates. To accurately answer the student's question, the provided spot rates would be imperative in working out the correct calculation.