Final answer:
The face value of a zero-coupon bond is calculated using the purchase price, the yield or interest rate, the number of times interest is compounded per year, and the number of years to maturity.
Step-by-step explanation:
Finding the Face Value of a Zero-Coupon Bond
To find the face value of a zero-coupon bond, we first need to understand what a zero-coupon bond is. A zero-coupon bond is a bond that does not pay periodic interest payments. Instead, it is sold at a discount to its face value and pays the full face value at maturity. The face value, also known as the par value, is the amount the issuer agrees to pay the bondholder when the bond matures.
The question at hand is to find the face value of a 10-year zero-coupon bond with a yield of 5.9% compounded semiannually, and a purchase price of $18,000. The formula to calculate the face value of a bond given the price, rate, and time is:
Face Value = Price * (1 + (rate/n))^(n*t)
Where:
- Price is the current price of the bond.
- Rate is the yield or interest rate.
- n is the number of times interest is compounded per year.
- t is the number of years to maturity.
In this scenario, n = 2 (since interest is compounded semiannually), t = 10, and the rate is 5.9% or 0.059. Plugging these values into the formula gives us:
Face Value = $18,000 * (1 + (0.059/2))^(2*10)
By calculating this expression, we can find the face value of the bond. Round off this final value to the nearest dollar as required to provide the answer.
Conceptually, understanding the relationship between the face value, the bond's price, and the interest rate is crucial in finance. When interest rates rise, bonds previously issued at lower interest rates will sell for less than face value. Conversely, when interest rates fall, bonds previously issued at higher interest rates will sell for more than face value.