Final answer:
To find the interest earned on a $50,000 deposit for six years at 4% interest, compounded continuously, we use the formula for compound interest. Plugging in the values and evaluating the expression, the final amount is approximately $63,388.61. Subtracting the principal from the final amount gives us the interest earned, which is $13,388.61.
Step-by-step explanation:
The compound interest can be defined as interest you earn on interest. With a savings account that earns compound interest, you earn interest on the principal (the initial amount deposited) plus on the interest that accumulates over time.
To find the interest earned on a $50,000 deposit for six years at 4% interest, compounded continuously, we will use the formula for compound interest: A = P * e^(rt), where A is the final amount, P is the principal, r is the interest rate (in decimal form), t is the time in years, and e is a mathematical constant approximately equal to 2.71828.
Plugging in the values, we have A = 50000 * e^(0.04 * 6).
Using a calculator or online tool to evaluate this expression, we find that the final amount is approximately $63,388.61. To find the interest earned, we subtract the principal from the final amount: Interest = $63,388.61 - $50,000 = $13,388.61.