A bond has a coupon rate of 8% per annum with interest paid semi-annually. The bond's face value is Rs 1000 and it matures in 5 years. If the bond is prices to yield 8% P.a. What is the bond's current price ?

₹1000

The correct answer is option (2) :₹1000

Given $ F= ₹1000$

$r=\frac{8}{2}$%= 4% per half year

$N= 5×2=10 $ half year

$d=\frac{8}{2}$ %= 4% per half year

$∴i=0.04$

So, coupon payment

$C=F×\frac{r}{100}$

$=1000×\frac{4}{100}$

$=₹40$

Now, P.V $=\frac{C[1-(1+i)^{-n}]}{i}+F(1+i)^{-N}$

$=40\left[\frac{1-(1.04)^{-10}}{0.04}\right]+1000(1.04)^{-10}$

Let $x= (1.04)^{-10}$

Taking log on both sides

$log\, x = -10log 1.04$

$=-10×0.0170$

$log\, x = -0.1700$

$log\, x = T.8300$

$x= antilog\, T.8300$

$x= 0.671 $

So, $P.V=\frac{40[1-0.6761]}{0.04}+1000×0.6761$

$=323.90+676.10$

$=₹1000$