On 1 January 2011 a company issued five-year fixed-interest bonds with a face value of $5 million, paying half-yearly coupons at 8.25 per cent per annum. Coupons are payable on 30 June and 31 December each year until maturity. On 15 September 2013 the holder of the bonds sells at a current yield of 8.63 per cent per annum. Calculate the price at which the investor sold the bond.

The price at which the investor sold the bond equals the Present Value of the Interest and the Face Value to be $4,975,447.20.

Data and Calculations:

Face value of bonds = $5,000,000

Interest rate = 8.25% per year

Half-yearly interst payment = $206,250 ($5,000,000 x 8.25% x 1/2)

Interest payment = half-yearly

Interest payment dates = June 30 and December 31

Interest paid on the bonds = $1,031,250 ($5,000,000 x 8.25% x 2.5)

Interest to be paid on the bonds = $1,031,250 ($5,000,000 x 8.25% x 2.5)

Current yield of the bonds = 8.63% per annum

PV of interests to be paid at 8.63% p.a for 2.5 years = $910,119.53

PV of bonds face value at 8.63% p.a for 2.5 years = $4,065,327.67

Price of the bonds = $4,975,447.20 ($4,065,327.67 + $910,119.53)

Thus, the investor sold the bond at $4,975,447.20.

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