Question

Brown Enterprises’ bonds currently sell for $1,025. They have a 9-year maturity, an annual coupon of $80, and a par value of $1,000. What is their current yield?

Answer 1

So the present value
= 1000(1+i)^-9 + 80(1 - (1+i)^-9 )/i

so 1000(1+i)^-9 + 80(1 - (1+i)^-9 )/i = 1025

A very nasty equation to solve.

I tried a few values:
i = .08, RS = 1000 , looking for 1025
i = .09, RS = 940, so let's lower the i
i = .07, RS = 1065 , too low
i = .075, RS = 1031.894 getting closer
i = .077, RS = 1018.977

ok, so i is between .075 and .077

.075 .... 1031.894
i ...........1025
.077 ......1018.977

use interpolation by setting up a ratio

(i - .075)/(.077-.075) = (1025-1031.894)/(1018.977-1031.894)

I will leave the arithmetic up to you, but I got
i = .07607