Question

# Determine the purchase price at the indicated time before the maturity of the following bond redeemed...

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.)

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

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