Final answer:
The yield to maturity on a four-year zero-coupon bond purchased today would be 12%, considering both interest payments and capital gains, when the bond is bought for $964 and pays out $1,080 ($1,000 face value plus an $80 interest payment) at maturity.
Step-by-step explanation:
The yield to maturity (YTM) on a four-year zero-coupon bond purchased today would represent the bond's total return, considering both interest payments and capital gains. Calculating this yield involves knowing the bond's face value, purchase price, and maturity value. Consider a bond with a $1,000 face value that is purchased for $964. By the end of four years, the investor receives the face value. The yield to maturity in this scenario would be calculated as (($1,000 + $80) - $964)/$964 = 12%. This calculation assumes an interest or coupon rate of 8%, and that the investor receives an $80 interest payment in the last year.
It is important to understand that bond prices and interest rates have an inverse relationship. When interest rates rise, the value of existing bonds with lower interest rates decreases, causing them to sell for less than their face value. Conversely, when interest rates drop, bonds with higher interest rates become more valuable and may sell for more than their face value.