To find the yield rate and coupon rate of a ten-year bond priced at $9,906.38, with a present value of redemption value of $6,142.34 and a coupon rate to yield ratio of 2/3, first calculate the yield rate by subtracting the present value of redemption value from the bond price, then calculating the annual coupon payment using the yield rate, and finally converting the yield rate to a percentage. The yield rate is approximately 61.27%. Next, find the coupon rate by multiplying the yield rate by 2/3. The coupon rate is approximately 40.82%.
To find the yield rate and coupon rate of a ten-year bond, we need to use the available information. The bond is priced at $9,906.38, which is the present value of all the future cash flows. The present value of the redemption value is $6,142.34. The coupon rate to yield ratio is 2/3.
Using these values, we can calculate the yield rate as follows:
- First, we subtract the present value of the redemption value from the bond price: $9,906.38 - $6,142.34 = $3,764.04
- Next, we calculate the annual coupon payment by multiplying the yield rate (Y) by the redemption value: Y * $6,142.34 = $3,764.04
- Then, we solve for Y: Y = $3,764.04 / $6,142.34 ≈ 0.6127
- Finally, we convert Y to a percentage to get the yield rate: 0.6127 * 100 ≈ 61.27%
Now, let's find the coupon rate using the ratio provided:
- Since the ratio of the coupon rate to the yield is 2/3, we multiply the yield rate by 2/3: 61.27% * 2/3 ≈ 0.4082
- Thus, the coupon rate is approximately 0.4082, or 40.82%
Complete Question :
A ten-year $10,000 face value bond with annual coupons is priced at $9,06.38. The present value of the redemption value is $6,142.34 and the ratio of the coupon rate to the yield is 2/3. Find the yield rate and coupon rate.