Final answer:
The rate of return on the bond if its yield to maturity at the end of the year is 12% will be calculated using the formula: (($1000 + $80) - $964)/$964, resulting in a return of 12%. This return includes both the last year's interest and any capital gains or losses on the bond.
Step-by-step explanation:
The question pertains to calculating the rate of return on a 2-year maturity bond with specified annual coupon payments and yield to maturity conditions.
The rate of return on a bond considers not only the interest payments, or coupons, received but also any capital gains or losses when the bond is sold relative to its purchase price. If the bond is sold for more or less than the purchase price, capital gains or losses occur, respectively.
Assuming that the yield to maturity at the end of the year is 12%, and the bond makes a last year's interest payment of $80, an investor will receive a total of $1,080 ($1,000 face value plus $80 interest).
If the bond is currently selling at $964 (as an example where the interest rates have risen, causing the bond to sell for less than face value), the rate of return will be calculated as (($1080 – $964)/$964) = 12%.
This example illustrates the inverse relationship between bond prices and yield to maturity: when interest rates increase, the market value of existing bonds with lower coupon rates decreases, and when interest rates decrease, bonds with higher coupon rates increase in market value.