Question

A 12-year, 5% coupon bond pays interest annually. The bond has a face value of $1,000. Blank 1. Fill in the blank, read surrounding text. -12.38 % is the percentage change in the price of this bond if the yield to maturity rises to 6% from the current yield to maturity of 4.5%?

Answer 1

The answer is "12.38 %".

Step-by-step explanation:

Please find the complete question in the attached file.

Price of face
`= \$ \ 1,000`

Yearly Coupon Rate
`= 5 \%`

Yearly Coupon
`= \$ \ 1,000 * 5 \%`

`= \$ \ 50`

Maturity time
`= 12 \ years`

Bond yield
`= 4.5 \%`

Price
`= \$ \ 50 * PVIFA(4.50 \%, 12) + \$ \ 1,000 * PVIF(4.50 \%, 12)`

`= \$ \ 50 * ((1-( (1)/(1.045))^(12)))/(0.045) + (1,000)/(1.045^(12))\\\\= \$ \ 1,045.59`

Returns shift to
`6 \%`

Price
`= \$ 50 * PVIFA(6 \%, 12) + \$ 1,000 * PVIF(6 \%, 12)`

`= \$ 50 * ((1-((1)/(1.06))^(12)))/(0.06) + (1,000)/(1.06^(12))\\\\= \$ \ 916.16`

Shift in prices:

`= ((\$ \ 916.16 - \$ \ 1,045.59))/(\$ \ 1,045.59) \\\\ = -12.38 \%`OR
`=12.38 \%`