Ms. Sheela creates a fund of ₹1,00,000 for providing scholarships to needy children. The scholarship is provided in the beginning of the year. This fund earns an interest of r% per annum. If the scholarship amount is taken as ₹8,000, then r =

$8 \frac{16}{23}$%

The correct answer is Option (2) → $8 \frac{16}{23}$%

$\text{Present value of perpetuity due}=100000.$

$\text{Annual scholarship }=8000.$

$100000=8000\left(\frac{1+r}{r}\right).$

$\frac{1+r}{r}=\frac{100000}{8000}=12.5.$

$1+r=12.5r.$

$11.5r=1.$

$r=\frac{1}{11.5}=\frac{2}{23}.$

$r=0.08696.$

$r=8.7\%.$