If the cash equivalent of a perpetuity of ₹1200 payable at end of each half year is ₹96,000, the annual rate of interest compounded half yearly is :
Answer & explanation
Correct answer: option 2
$\text{Present value of perpetuity}=96000.$
$\text{Payment each half year}=1200.$
$\text{For perpetuity: }PV=\frac{R}{i}.$
$96000=\frac{1200}{i}.$
$i=\frac{1200}{96000}.$
$i=0.0125.$
$\text{Half-yearly rate}=1.25\%.$
$\text{Annual nominal rate (compounded half yearly)}=2\times1.25\%.$
$=2.5\%.$
$\text{Annual rate of interest}=2.5\%.$