Question

Dexter Mills issued 20-year bonds a year ago at a coupon rate of 11.4 percent. The bonds make semiannual payments. The yield-to-maturity on these bonds is 9.2 percent. What is the current bond price? (show work)

$991.90

$985.55

$1,192.16

$1,195.84

$1,198.00

Answer 1

The current bond price is computed as shown below:

Coupon payments is computed as follows:

= 11.4% / 2 x $ 1,000

= $ 57

N = 19 x 2 (Since one year has lapsed and coupon payments are semi annual )

= 38

YTM = 9.2% / 2

= 4.6%

So the current bond price will be:

= $ 57 / 1.046¹ + $ 57 / 1.046² + $ 57 / 1.046³ + $ 57 / 1.046⁴ + $ 57 / 1.046⁵ + $ 57 / 1.046⁶ + $ 57 / 1.046⁷ + $ 57 / 1.046⁸ + $ 57 / 1.046⁹ + $ 57 / 1.046¹⁰ + $ 57 / 1.046¹¹ + $ 57 / 1.046¹² + $ 57 / 1.046¹³ + $ 57 / 1.046¹⁴ + $ 57 / 1.046¹⁵ + $ 57 / 1.046¹⁶ + $ 57 / 1.046¹⁷ + $ 57 / 1.046¹⁸ + $ 57 / 1.046¹⁹ + $ 57 / 1.046²⁰ + $ 57 / 1.046²¹ + $ 57 / 1.046²² + $ 57 / 1.046²³ + $ 57 / 1.046²⁴ + $ 57 / 1.046²⁵ + $ 57 / 1.046²⁶ + $ 57 / 1.046²⁷ + $ 57 / 1.046²⁸ + $ 57 / 1.046²⁹ + $ 57 / 1.046³⁰ + $ 57 / 1.046³¹ + $ 57 / 1.046³² + $ 57 / 1.046³³ + $ 57 / 1.046³⁴ + $ 57 / 1.046³⁵ + $ 57 / 1.046³⁶ + $ 57 / 1.046³⁷ + $ 57 / 1.046³⁸ + $ 1,000 / 1.046³⁸

= $ 1,195.84 Approximately

So the correct answer is option of $ 1,195.84

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