I need help finding the YTM of a bond

Question

Ngata Corp. issued 12-year bonds 2 years ago at a coupon rate of 9.6 percent (APR). The bonds make semiannual payments. If these bonds currently sell for 99 percent of par value, what is the YTM (as an APR)?

 

4.88%
11.71%
10.73%
9.76%
8.78%

Answer 1

The bonds have 10 years to go, or 20 periods, they pay $48 every six months and $1,000 at maturity. The present value of that stream of payments is $990. So you have to find the discount rate that discounts the payment stream to $990. This is easily done with a financial calculator. But you can do it by discounting the maturity value and the interest annuity by assuming an approximate discount rate, solve for the present value, then adjust the discount rate up or down by small amounts until the present value for the rate you selected is $990. This trial and error method can zero in on the correct rate with a small number of tries. Start with 9.5%, then increase it until you get the 9.67 rate that gives you the $990 present value of the two streams of payments.