A well$-$known industrial firm has issued $$1000$ bonds that carry $4\%$ nominal annual interest paid semiannually. The bonds mature $20$ years from now, at which

time the industrial firm will redeem them for face value plus the terminal semiannual interest payment. From the financial pages of your newspaper you learn that

the bonds may be purchased for $$715$ each $($ $$710$ for the bond plus a $$5$ sales commission$).$ What nominal annual rate of return would you receive if you

purchased the bond now and held it to maturity $20$ years from now?

Solution:

$NPW=PW$ of Benefits $-PW$ of Costs $=0$

Interest received every half year is $A=$$

Number of compounding period $n=$

$PW$ of Benefits $=A(\frac{P}{A},i^{**},n)+F(\frac{P}{F},i^{**},n)$;

$PW$ of Costs $=$

Find out $i^{**}$ using trial and error

Try $i=3\%$:$NPW=$

Try $i=3\mathrm{.}5\%$:$NPW=$

Performing linear interpolation: $i^{**}=,\%$

Find nominal and effective rate:

Nominal rate $r=$

Effective rate $i_a=$

$\%.$