Final answer:
Malcolm's balance will take approximately 15.1 years to double in an account that pays 4.6% interest rate compounded continuously.
Step-by-step explanation:
To find out how long it will take for Malcolm's balance to double, we can use the formula for continuous compounding: A = P * e^(rt), where A is the future balance, P is the initial deposit, r is the interest rate, t is the time in years, and e is the base of the natural logarithm. In this case, we need to solve for t. Let's plug in the given values: 2P = P * e^(0.046t). We can cancel out the P on both sides of the equation. Now, we have 2 = e^(0.046t). To solve for t, we take the natural logarithm (ln) of both sides: ln(2) = ln(e^(0.046t)). Using the property of logarithms, we can bring down the exponent of e: ln(2) = 0.046t * ln(e). Note that ln(e) is equal to 1. Therefore, we can rewrite the equation as ln(2) = 0.046t. To isolate t, we divide both sides by 0.046: t = ln(2) / 0.046. Evaluating this expression, we find that t ≈ 15.1 years.