A bond has a face value of Rs 10000, a coupon rate of 10,.75% p.a. paid semi-annually and mature in 5 years. If the yield to maturity is 10% , find the current price of the bond.

₹10289.65

The correct answer is option (2):₹10289.65

Given $F= ₹10000, r= 10.75$ % = 5375 % per half year

$N= 10$ half years

$d=\frac{10}{2}$% half year $⇒ i = 0.05 $

$C= F×\frac{r}{100}$

$=1000×\frac{5.375}{100}$

$=₹537.5$

$P.V=\frac{537.5[1-(1.05)^{-10}]}{0.05}+1000(1.05)^{-10}$

Let $ x= (1.05)^{-10}$

Taking log on both sides, we get

$log\, x =-10log\, 1.05$

$=-10×0.0212$

$=-0.2120$

$log\, x = I. 7880$

$x= antilog\, I.7880$

$x= 0.6138$

$P.V=\frac{53,75[1-0.6138]}{0.05}+10000×0.6138$

$=₹4151.665+₹6138$

$=₹10289.65$