Zero-Coupon Bond Price Calculation

What is the price of a zero-coupon bond with a $1000 face value and a yield to maturity of 10.4% with ten years left until maturity?

A) $372

B) $1040

C) $1000

D) $602

Answer

The price of this zero-coupon bond is closest to D) $602.

To calculate the price of a zero-coupon bond, we use the formula:

Price = Face Value / (1 + YTM)^N

Where:

Face Value is the future value or the maturity value of the bond ($1000 in this case).

YTM is the yield to maturity (10.4% in decimal form).

N is the number of periods until maturity (10 years in this case).

Plugging in the given values:

Price = $1000 / (1 + 0.104)^10

Calculating this expression gives a price closest to $602. Therefore, option D) $602 is the closest approximation of the bond's price.