Question

The Deltona Instrument Company has 9 percent coupon bonds on the market with 6 years left to maturity. The bonds make annual payments. If the bond currently sells for $974.60, what is its YTM?
8.82 percent
8.90 percent
8.98 percent
9.58 percent
9.63 percent

Answer 1

The Deltona Instrument Company has 9 percent coupon bonds on the market with 6 years left to maturity. The bonds make annual payments. If the bond currently sells for $974.60, what is its YTM?

8.82 percent

8.90 percent

8.98 percent

9.58 percent

9.63 percent

$$f(x) = 1000 + -974.6 * (1+x)^6 + 90 \left[ (1+x)^6 - 1 \right] / x$$ $$f'(x) = 6 * -974.6 * (1+x)^5 + 90 * (6 \times (1 + x)^5 - (1 + x)^6 + 1) / (x^2)$$ $$x = 0.1$$ $$f(x) = -32.1585$$ $$f'(x) = -7664.9133$$ $$x1 = 0.1 - -32.1585 / -7664.9133 = 0.0958044599538$$ $$\text{Error Bound} = 0.0958044599538 - 0.1 = 0.004196 > 0.000001$$ $$x1 = 0.0958044599538$$ $$f(x1) = -0.3356$$ $$f'(x1) = -7505.3769$$ $$x2 = 0.0958044599538 - -0.3356 / -7505.3769 = 0.0957597499751$$ $$\text{Error Bound} = 0.0957597499751 - 0.0958044599538 = 4.5E-5 > 0.000001$$ $$x2 = 0.0957597499751$$ $$f(x2) = -0$$ $$f'(x2) = -7503.6905$$ $$x3 = 0.0957597499751 - -0 / -7503.6905 = 0.0957597449509$$ $$\text{Error Bound} = 0.0957597449509 - 0.0957597499751 = 0 < 0.000001$$ $$\text{YTM} = 9.58\%$$ $$\text{Annual YTM} = 9.58\%$$