Complete Question:
Suppose a five-year, $1000 bond with annual coupons has a price of $903.35 and a yield to maturity of 5.6%. What is the bond's coupon rate?
Answer:
3.396% Approximately
Explanation:
We can calculate the coupon interest by using the formula given in the attachment.
Now, here we have:
F is the Face value which is $1000
P is the price of the bond which in this case is $903.35
C is the Coupon interest
n are the number of years which is 5 years in this case
Yield to Maturity is 5.6%
By putting the values in the given equation we have:
5.6% = [C + ($1000 - $903.35)/5 years] / [($1000 + $903.35)/2]
5.6% = [C + 19.33] / [951.675]
0.056 * 951.675 = C + 19.33
53.2938 = C + 19.33
C = 53.2938 - 19.33
C = $33.96 approximate estimate.
Now we will find the coupon rate by using the following formula:
Coupon Rate = Coupon Interest / Face Value
By putting values, we have:
Coupon Rate = $33.96 / $1000 = 3.396% Approximately.
Accurate Coupon interest can be calculated using excel. The above answer gives minor difference in decimal points.
The bond coupon rate when all things are given so it should be closest to the 3.396%.
Since
F is the Face value = $1000
P is the price of the bond = $903.35
C is the Coupon interest
n are the number of years = 5 years
Yield to Maturity = 5.6%
Now
5.6% = [C + ($1000 - $903.35)/5 years] / [($1000 + $903.35)/2]
5.6% = [C + 19.33] / [951.675]
0.056 * 951.675 = C + 19.33
53.2938 = C + 19.33
C = 53.2938 - 19.33
C = $33.96
Now the coupon rate is
Coupon Rate = Coupon Interest / Face Value
Coupon Rate
= $33.96 / $1000
= 3.396%
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