To calculate the new yield to maturity (YTM) on the bond, we can use the bond pricing formula:
Bond price = (Coupon payment / YTM) x (1 - 1 / (1 + YTM)^n) + Face value / (1 + YTM)^n
Where:
Bond price is the current market price of the bond ($1,128)
Coupon payment is the annual coupon payment (0.072 x $1,000 = $72)
YTM is the yield to maturity that we want to find
n is the number of years until maturity (10)
Using algebra, we can rearrange this formula to solve for YTM:
YTM = Coupon payment / [(Bond price - Face value) / (1 + (Face value / Bond price)^(1/n)) + 1 / (1 + (Face value / Bond price)^(1/n))]
Plugging in the values from the problem, we get:
YTM = $72 / [($1,128 - $1,000) / (1 + ($1,000 / $1,128)^(1/10)) + 1 / (1 + ($1,000 / $1,128)^(1/10))] ≈ 6.13%
Therefore, the new yield to maturity on the bond is approximately 6.13%.
To calculate the rate of return over the year, we need to consider both the coupon payments and the change in the bond price. The total return can be calculated as follows:
Total return = (Coupon payment + Change in bond price) / Initial bond price
Where:
Coupon payment is the annual coupon payment ($72)
Change in bond price is the increase in bond price over the year ($1,128 - $973 = $155)
Initial bond price is the price at which the bond was purchased ($973)
Plugging in the values from the problem, we get:
Total return = ($72 + $155) / $973 ≈ 24.1%
Therefore, the rate of return over the year is approximately 24.1%.