Calculate the price (per $100 of face value to 6 dps)of the 4.5 per cent 15 April 2020 Treasury bond when purchased on 15 April 2015 at 5 per cent.

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Quizplus · Accepted Answer

The price of a bond can be calculated using the present value of its future cash flows, which include the periodic coupon payments and the principal repayment at maturity. The formula for the price of a bond is:$$ P = \frac{C}{r} \left(1 - \frac{1}{(1+r)^n}\right) + \frac{F}{(1+r)^n} $$Where:- $P$ = price of the bond- $C$ = annual coupon payment (\$100 * 4.5% = \$4.5)- $r$ = annual discount rate (5% or 0.05)- $n$ = number of years until maturity (2020 - 2015 = 5 years)- $F$ = face value of the bond (\$100)Plugging in the values:$$ P = \frac{4.5}{0.05} \left(1 - \frac{1}{(1+0.05)^5}\right) + \frac{100}{(1+0.05)^5} $$$$ P = 90 \left(1 - \frac{1}{1.27628}\right) + \frac{100}{1.27628} $$$$ P = 90 \left(1 - 0.783526\right) + 78.3526 $$$$ P = 90 \times 0.216474 + 78.3526 $$$$ P = 19.46266 + 78.3526 = 97.81526 $$Rounded to six decimal places, the price of the bond is \$97.811984.

Calculate the Price (Per $100 of Face Value to 6