Question

You are thinking about buying a bond that offers a coupon rate of 6% but with semi-annual coupon payments. The bond has exactly 7 years remaining to maturity. The face value of the bond is $1,000. Your required return is 8.16% per year. How much should you be willing to pay for this bond? 1,211.2625

Answer 1

Present price of bond = $886.5165

Step-by-step explanation:

As for the information provided:

Coupon rate = 6% paid semiannually.

Interest = $1,000
`* (6)/(100) * (6)/(12)` = $30

Since paid semiannually, effective return rate = 8.16/2 = 4.08%

Time period = 7 years
`*` 2 = 14 periods

Future value of interest = Future annuity Value @ 4.08% for 14 periods =

`(1)/((1+0.0408)^1) +  (1)/((1+0.0408)^2) +  (1)/((1+0.0408)^3) +  (1)/((1+0.0408)^4) +  (1)/((1+0.0408)^5) + ............ +  (1)/((1+0.0408)^1^4)` = 10.50755

Interest value = $30
`*` 10.50755 = $315.2265

Principal = $1,000
`* (1)/((1 + 0.0408)^1^4)` = $1,000
`*` 0.57129

= $571.29

Present price of bond = $571.30 + $315.228 = $886.5165.