Final answer:
To determine the price of a zero-coupon, four-year, risk-free bond, calculate the present value of its $1,000 face amount using the current interest rate. If the interest rate is 12% with one year to maturity, the present value would be approximately $892.86, allowing for a 12% yield to the investor.
Step-by-step explanation:
To determine the price per face value of a four-year, zero-coupon, risk-free bond, we must first understand that a zero-coupon bond does not pay annual interest. Instead, it is sold at a discount and reaches its full face value at maturity. Considering a risk-free zero-coupon bond with a face value of $1,000, the price of the bond can be calculated using the prevailing interest rates. If we assume an interest rate of 12%, and there's one year left to maturity, we can use the formula for the present value of a single future cash flow:
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- Present Value = Future Value / (1 + interest rate)^number of periods
Using this formula:
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- Present Value = $1,000 / (1 + 0.12)^1
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- Present Value = $1,000 / 1.12
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- Present Value = $892.86 approximately
Therefore, the bond would be priced at approximately $892.86 to provide an investor with a 12% yield, reflecting market conditions where similar investments offer 12% returns.
Bond sellers will adjust prices in response to interest rate fluctuations to maintain an attractive yield for investors. When interest rates rise, the bond prices fall to ensure the bond's yield aligns with current market conditions. Conversely, when interest rates drop, bonds with higher coupon rates become more attractive, and their selling price can exceed the face value.