To find out how many years it will take for the bank deposit to yield \( 6.42 \times 10^4 \) in interest, we can set up the equation:
\[ \text{Total Interest} = \text{Annual Interest} \times \text{Number of Years} \]
Given that the annual interest is \( 802.50 \), we can express the total interest gained over the years as follows:
\[ 6.42 \times 10^4 = 802.50 \times t \]
Where \( t \) is the number of years. We need to solve for \( t \):
\[ t = \frac{6.42 \times 10^4}{802.50} \]
Calculating:
- First, calculate \( 6.42 \times 10^4 \):
\[ 6.42 \times 10^4 = 64200 \]
- Now, divide by \( 802.50 \):
\[ t = \frac{64200}{802.50} \approx 80 \]
Thus, it will take approximately 80 years for the bank deposit to yield \( 6.42 \times 10^4 \) in interest.