Question

A five-year bond with a face value of 1000 pays coupons semiannually. The bond is redeemable at face value. It is bought at issue at a price to produce an annual yield rate of 8.7% convertible semiannually. If the term of the bond is doubled and the yield rate remains the same, the purchase price would decrease by 44. Calculate the amount of a coupon.

Answer 1

To calculate the bond's coupon amount, use the given equations for both the original bond and the new bond. By plugging in the given values, you can solve for the amount of the coupon.

Step-by-step explanation:

Calculation of Bond Coupon Amount

Let's consider the original bond's price as P and the new bond's price as P'. Also, let the original coupon amount be C. According to the given information, the yield rate is 8.7%. Using the given equation (P - C)/(P) = 8.7%, we can solve for C.

We are then told that if the term of the bond is doubled and the yield rate remains the same, the purchase price would decrease by 44%. Let the purchase price of the new bond be P' and the coupon amount for the new bond be C'. Using the new information, we can use the equation (P' - C')/(P') = (100 - 44)/100 * 8.7%, to find the new coupon amount C'.

Now, let's solve the equations step by step:

Calculate the original coupon amount C by rearranging the equation to C = P(1 - 8.7%)

Solve for the new coupon amount C' using the equation C' = P'(1 - 0.44 * 8.7%)

Plug in the given values of P, P', and C' to calculate the amount of the coupon.