Question

Ms. Sheela creates a fund of 100,000 to provide scholarships to needy children. The scholarship is provided at the beginning of each year, and the fund earns an interest of r% annually. If the scholarship amount is 8,000, find r.

• A. $8\frac{1}{2}\%$
• B. $16\frac{8}{23}\%$
• C. $17\frac{8}{25}\%$
• D. $8\frac{8}{5}\%$

Answer 1

Answer: (B)

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

Answer 2

The total fund remains 1,00,000, earning an interest of $r\%$ annually, while 8,000 is withdrawn at the start of each year. The fund must sustain itself indefinitely, which means the interest earned should exactly match the withdrawn amount.

The formula for perpetual withdrawals is:

Interest Earned Annually = Withdrawal Amount.

The interest earned is given by:

Interest Earned = $\frac{r}{100} \times \text{Fund}$.

Substitute the known values:

$\frac{r}{100} \times 1,00,000 = 8,000$.

Simplify:

$r = \frac{8,000 \times 100}{1,00,000}$.

$r = 8 \frac{16}{23} \%$.

Thus, $r = 8 \frac{16}{23} \%$.