Question

Alice invests $15,000 at age 30 from the singing bonus of her new job. She hopes the investment will be worth $30,000 when she turns 40. If the interest compounds continuously, approximately what rate of growth will she need to achieve her goal? Round your answer to the nearest tenth.

Answer 1

To achieve her investment goal, Alice will need an approximate rate of growth of 7.2%

Step-by-step explanation:

To calculate the rate of growth required for Alice to achieve her investment goal, we can use the formula for compound interest which is A = P*e^(rt), where A is the future value, P is the principal amount, e is Euler's number (approximately 2.71828), r is the interest rate, and t is the time in years. In this case, Alice wants her investment of $15,000 to grow to $30,000 in 10 years.

Plugging in the values, we have 30000 = 15000*e^(r*10). We can rearrange this equation to r = (1/10) * ln(2), where ln is the natural logarithm. Using this formula, the approximate rate of growth Alice will need is 7.2%.