When dealing with perpetual withdrawals, it’s essential to balance the interest earned with the withdrawal amount. The formula \( \text{Interest Earned} = \frac{r}{100} \times \text{Fund} \) allows us to find the interest rate needed to match the annual withdrawals. It’s important to solve the equation step by step, ensuring to simplify fractions and percentages correctly. This will help ensure that the fund continues to sustain itself without running out of money.
The total fund is 1,00,000, which earns an annual interest of \( r\% \). An amount of 8,000 is withdrawn at the beginning of each year. For the fund to be sustainable indefinitely, the annual interest earned must equal the annual withdrawal.
The condition for perpetual withdrawals is:
Annual Interest Earned = Withdrawal Amount.
The annual interest earned is calculated as:
Interest Earned = \( \frac{r}{100} \times \text{Fund Value} \).
Substituting the given values:
\( \frac{r}{100} \times 1,00,000 = 8,000 \).
Simplifying the equation to solve for \( r \):
\( r = \frac{8,000 \times 100}{1,00,000} \).
\( r = 8 \frac{16}{23} \% \).
Therefore, the required interest rate is \( r = 8 \frac{16}{23} \% \).