Question

Violet is going to invest $1,800 and leave it in an account for 6 years. Assuming the interest is compounded continuously, what interest rate, to the nearest tenth of a percent, would be required in ord er for Violet to end up with $2,400?​

Answer 1

To determine the interest rate required for Violet to end up with $2,400 after 6 years of continuously compounded interest, use the formula A = P * e^(rt). Plugging in the given values and solving for r gives an interest rate of approximately 8.05%.

Step-by-step explanation:

To determine the interest rate required for Violet to end up with $2,400 after 6 years of continuously compounded interest, we can use the formula:

A = P * e^(rt)

Where:

• A is the final amount ($2,400)
• P is the initial investment ($1,800)
• r is the interest rate we want to find
• t is the time in years (6 years)

Plugging in the given values, the equation becomes:

$2,400 = $1,800 * e^(6r)

To solve for r, we can divide both sides of the equation by $1,800 and then take the natural logarithm (ln) of both sides:

ln($2,400/$1,800) = 6r

r = ln($2,400/$1,800) / 6

Calculating this expression gives an interest rate of approximately 0.0805, or 8.05% to the nearest tenth of a percent.