Final answer:
To find the face value of the zero-coupon bond, use the present value formula with the given purchase price, term, and discount rate. The face value calculation reveals that the bond will worth $14279.63 when it matures in 17 years.
Step-by-step explanation:
To find the face value of a zero-coupon bond, we need to calculate the present value of the bond using the information given. Since the bond is zero-coupon, it does not pay interest until maturity; instead, it is sold at a discount and then pays its face value at maturity. We know the current price of the bond is $7000, the bond term is 17 years, and the discount rate (yield to maturity) is 3.2% compounded semiannually.
The formula to calculate the present value of a zero-coupon bond is:
P = F / (1 + r/n)nt
Where:
- P is the current price of the bond ($7000)
- F is the face value we are looking to find
- r is the annual discount rate (0.032)
- n is the number of times interest is compounded per year (2)
- t is the number of years until maturity (17)
Plugging in these values and solving for F, we get:
F = $7000 * (1 + 0.032/2)2*17
F = $7000 * (1 + 0.016)34
F = $7000 * (1.016)34
F = $7000 * 2.0399475
F = $14279.63 (rounded to two decimal places)
Therefore, the face value of the zero-coupon bond will be $14279.63.