A $25 000, 10% bond redeemable at par on December 1, 2025, is purchased on September 25, 2014, to yield 7.6% compounded semi-annually. Bond interest is payable semi-annually.
25,000 x 10% = 500
500 x 10 months = 3,000
3,000 x 7.6% = 650
= 650 + 500 = 4,000
Answer is 4,000 easy
No need to thank me
To analyze this bond, we need to calculate its purchase price, yield to maturity, and the semi-annual interest payments.
First, let's calculate the semi-annual interest payment. The bond has a face value of $25,000 and an annual coupon rate of 10%. Since the interest is payable semi-annually, we need to divide the annual coupon rate by 2.
Annual coupon payment = Face value * Annual coupon rate
Semi-annual coupon payment = Annual coupon payment / 2
Semi-annual coupon payment = $25,000 * 10% / 2 = $1,250
Next, we need to determine the number of semi-annual periods remaining until maturity. The bond was purchased on September 25, 2014, and matures on December 1, 2025, which gives us a total of 22 semi-annual periods remaining until maturity.
Now, let's calculate the yield to maturity (YTM). The YTM is the yield or rate of return an investor would receive by holding the bond until maturity. In the case of this bond, the YTM represents the rate at which the bond is discounted to the purchase price.
To calculate YTM, we need to use the bond pricing formula, which is the present value of the bond's future cash flows (coupon payments and face value) discounted at the yield to maturity rate.
Purchase price = Semi-annual coupon payment * (1 - (1 + YTM/2)^-n) / (YTM/2) + Face value / (1 + YTM/2)^n
Where:
- Semi-annual coupon payment is $1,250
- YTM is the yield to maturity rate we are trying to find
- n is the number of semi-annual periods remaining until maturity (22)
By solving for YTM in the above equation, we can determine the yield to maturity rate that makes the purchase price equal to the present value of the bond's future cash flows.
Lastly, we can calculate the purchase price by plugging in the values for the semi-annual coupon payment, YTM, and number of periods into the bond pricing formula.
Once we have the purchase price, yield to maturity, and semi-annual interest payments, we can proceed with analyzing the bond further based on these values.