Explanation:
To calculate the annual interest, we first need to find the coupon rate of the bond, which is the interest rate that the bond pays annually on its face value.
The bond is a $1000 Treasury bond, which means its face value is $1000. The current yield of the bond is 3.99%, but this refers to the yield based on the current market price of the bond, which is quoted at 105 points.
To find the coupon rate, we can use the following formula:
Coupon rate = Annual interest payment / Face value
We know the face value is $1000, so we need to find the annual interest payment. To do this, we can use the following formula:
Annual interest payment = Face value x Coupon rate
We can rearrange this formula to solve for the coupon rate:
Coupon rate = Annual interest payment / Face value
Plugging in the values we know, we get:
Coupon rate = Annual interest payment / $1000
Annual interest payment = Coupon rate x $1000
Now we need to find the coupon rate. Since the current yield of the bond is 3.99%, we can assume that the coupon rate is close to this value. However, the current yield is based on the bond's market price, which is quoted at 105 points.
To convert the quoted price to a dollar value, we can use the following formula:
Bond price = Face value x Quoted price / 100
Plugging in the values we know, we get:
$1050 = $1000 x Quoted price / 100
Quoted price = 105
So the bond is quoted at 105 points, which means its price is $1050. Now we can use this price to estimate the coupon rate.
We know that the bond's annual interest payment is equal to its coupon rate times its face value, which is $1000. We also know that the bond's market price is $1050, which means that investors are willing to pay more than the face value to buy the bond. This suggests that the bond's coupon rate is higher than its current yield of 3.99%, since investors are willing to pay more than the face value to receive its interest payments.
To estimate the coupon rate, we can use the following formula:
Coupon rate = Annual interest payment / Bond price
Plugging in the values we know, we get:
Coupon rate = Annual interest payment / $1050
We need to solve for the annual interest payment, so we can rearrange the formula:
Annual interest payment = Coupon rate x $1050
We know that the current yield of the bond is 3.99%, so let's assume that the coupon rate is close to this value. To estimate the coupon rate, we can add a small percentage to the current yield, since the bond's market price suggests that its coupon rate is higher than its current yield.
Let's add 0.1% to the current yield to estimate the coupon rate:
Coupon rate = 3.99% + 0.1% = 4.09%
Plugging this into the formula, we get:
Annual interest payment = 4.09% x $1050 = $42.945
Rounding to the nearest cent, the annual interest payment is $42.95. Therefore, the answer is:
The annual interest on the bond is $42.95.