Find the current price of a bond of face value Rs 1000 coupon rate 7.5% p.a. paid semi-annually matures in 10 years and yield to maturity is 9% p.a.

₹902.50

The correct answer is option (4) : ₹902.50

Given $F= ₹1000, r=\frac{7.5}{2}$%=3.75 % per half year

$N= 10×2=20$ half year

$d=\frac{9}{2}$% = 4.5% per half year

$i= 0.045 $

$C=F×\frac{r}{100}=\frac{1000×3.75}{100}=₹37.5$

$P.V.\frac{37.[1-(1.045)^{-20}]}{0.045}+1000(1.045)^{-20}$

Let $x= (1.045)^{-20}$

Taking log on both sides

$log\, x = -20 \log 1.045 $

$log\, x = -20 ×0.091 $

$log\, x = -0.3820$

$log\,x= T.6180$

$x= antilog\, T.6180=0.4150$

$P.V.=\frac{37.5[1-0.4150]}{0.045}+1000×(0.4150)$

$=₹487.50+₹415$

$=₹902.50$