Final answer:
To find the interest rate, we use the continuous compound interest formula and isolate the interest rate. The interest rate required for Rashaad to end up with $9,200 after 6 years is approximately 3.86%.
Step-by-step explanation:
To find the interest rate needed for Rashaad to end up with $9,200 after 6 years, we can use the continuous compound interest formula: A = P * e^(rt), where A is the final amount, P is the principal amount (initial investment), e is Euler's number (approximately 2.71828), r is the interest rate, and t is the time in years.
In this case, we have A = $9,200, P = $8,300, and t = 6 years. Substituting these values into the formula, we get: $9,200 = $8,300 * e^(6r).
To solve for r, we need to isolate it. Dividing both sides of the equation by $8,300 gives us: e^(6r) = $9,200 / $8,300. Taking the natural logarithm (ln) of both sides will help us isolate r: ln(e^(6r)) = ln($9,200 / $8,300). Using the property of logarithms that ln(e^x) = x, we can simplify the equation to: 6r = ln($9,200 / $8,300). Finally, dividing both sides by 6 gives us the interest rate: r = ln($9,200 / $8,300) / 6.
Calculating this gives r ≈ 0.0386. Multiplying by 100 to express it as a percentage, the interest rate required for Rashaad to end up with $9,200 after 6 years is approximately 3.86%.