Final answer:
To calculate the price of a zero-coupon bond that matures in 16 years with a market interest rate of 3.6% and semiannual compounding, use the formula P = F / (1 + r/n)^(n*t). Plugging in the values, the price comes out to be approximately $590.55.
Step-by-step explanation:
To calculate the price of a zero-coupon bond, you can use the formula:
P = F / (1 + r/n)^(n*t)
Where:
- P is the bond price
- F is the maturity value or face value of the bond
- r is the market interest rate
- n is the number of compounding periods per year (for semiannual compounding, n would be 2)
- t is the number of years until maturity
In this case, the bond matures in 16 years, the market interest rate is 3.6%, and the bond is assumed to have semiannual compounding. Let's plug in the values:
P = 1000 / (1 + 0.036/2)^(2*16)
P = 1000 / (1.018)^(32)
P = 1000 / (1.69283)
P ≈ $590.55
Therefore, the price of the zero-coupon bond is approximately $590.55 when it matures in 16 years with a market interest rate of 3.6% and semiannual compounding.