If zero-coupon bonds are available that have an implied interest rate of 5 percent and a face value of $30,000, what is the approximate purchase price for those bonds?

Question

Quizplus · Accepted Answer

To calculate the purchase price of the zero-coupon bond, we can use the formula: 
Purchase price = Face value / (1 + implied interest rate)^number of years.

Since zero-coupon bonds have no coupon payments, the number of years is equivalent to the time to maturity.

If the implied interest rate is 5 percent, we can calculate the time to maturity as follows:

1 + 0.05 = (1 + r)^t
1.05 = (1 + r)^t

Assuming the time to maturity is 10 years:
t = 10 
1.05 = (1 + r)^10 
1.05^(1/10) - 1 = r
r = 0.0476

Therefore, the purchase price of the bond would be calculated as follows:

Purchase price = $30,000 / (1 + 0.0476)^10 = $28,571.43

Therefore, the best choice is A.

If Zero-Coupon Bonds Are Available That Have an Implied Interest