Question

Determine the purchase price at the indicated time before the maturity of the following

bond redeemed at par shown in the table below.

Par-Value	Bond Rate Payable​ Semi-Annually	Time Before Redemption	Yield Rate	Conversion Period
​$ 41,000	8​%	7 years	8.5%	quarterly

The purchase price of the bond is $__.

​(Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as​ needed.)

Answer 1

Face value = $41000

Coupon rate is 8%

Payable semiannually. So coupons in year = 2

Coupon payment = Face value*coupon rate*1/coupons in year

=41000*8%*1/2

=1640

Number of semiannual period in year (n) = 7*2

=14

Rate converitable quarterly = 8.5%

quarterly rate = 8.5%/4 =0.02125

Effective semiannual rate = ((1+quarterly rate)^number of quarters in semiannula period)-1

=((1+0.02125)^2)-1

=0.0429515625

so i = 0.0429515625

Bond price formula = Coupon amount * (1 - (1/(1+i)^n)/i + face value/(1+i)^n

=(1640*(1-(1/(1+0.0429515625)^14))/0.0429515625) + (41000/(1+0.0429515625)^14)

=39746.26551

So purchase price of bond is $39746.27