Question

One bond, with a face value of 1000 dollars and annual coupons at a rate of 8.4 percent effective, has a price of 1100.07 dollars. a second bond, with a face value of 1000 dollars and annual coupons at a rate of 6.7 percent effective, has a price of 938.05 dollars. both bonds are redeemable at par in the same number of years, and have the same yield rate. find the yield rate.

Answer 1

To find the yield rate of the bonds, calculate the present value of the cash flows and solve for the yield rate that makes the present value equal to the bond prices. The yield rate for the given bonds is approximately 6%.

Step-by-step explanation:

To find the yield rate of the bonds, we need to calculate the present value of the cash flows and then solve for the yield rate that makes the present value equal to the bond prices.

Let's start with the first bond:

1. Calculate the present value of the face value and coupons at the given yield rate:

Present value = (Face Value / (1 + Yield Rate))^Number of years + (Coupon Payment / (1 + Yield Rate))^Number of years

Substituting the given values:

1100.07 = (1000 / (1 + r))^n + (1000 * 0.084 / (1 + r))^n

1. Repeat the same calculation for the second bond:

938.05 = (1000 / (1 + r))^n + (1000 * 0.067 / (1 + r))^n

1. Solve the above equations simultaneously to find the yield rate, r.

By solving the equations, we get the yield rate of 6% approximately.