Double your wealth. Kant Miss Company is promising its investors that it will double their money every 6 years. What annual rate is Kant Miss promising? Is this investment a good deal? If you invest \( \$ 200 \) now and Kant Miss is able to deliver on its promise, how long will it take your investment to reach \( \$ 28,000 \) ? Using the Rule of 72 , what annual rate is Kant Miss promising? \( \square \% \) (Round to the nearest whole percentage.)

To determine the annual rate Kant Miss Company is promising, we can use the Rule of 72. The Rule of 72 states that you can estimate the time it takes for an investment to double by dividing 72 by the annual interest rate. Since Kant Miss doubles your investment every 6 years, we can set up the formula as follows: \[ 72 \div \text{Annual Rate} = 6 \] Solving for the annual rate gives: \[ \text{Annual Rate} = 72 \div 6 = 12\% \] So, Kant Miss is promising an annual rate of approximately \( 12\% \). Now, for your investment of \( \$200 \) to grow to \( \$28,000 \) using the double-rate promise, we can first calculate how many times it needs to double: \[ \frac{28,000}{200} = 140 \text{ (the investment needs to increase by a factor of 140)} \] In terms of doubling, \( 140 \) isn't a power of \( 2 \), but if we keep doubling, we first calculate the number of doublings needed. Each doubling multiplies your investment by \( 2 \): 1st doubling: \( 200 \times 2 = 400 \) 2nd doubling: \( 400 \times 2 = 800 \) 3rd doubling: \( 800 \times 2 = 1600 \) 4th doubling: \( 1600 \times 2 = 3200 \) 5th doubling: \( 3200 \times 2 = 6400 \) 6th doubling: \( 6400 \times 2 = 12800 \) 7th doubling: \( 12800 \times 2 = 25600 \) It takes \( 7 \) doublings, which corresponds to \( 7 \times 6 = 42 \) years to reach or surpass \( 28,000 \). In conclusion, Kant Miss Company promises an annual rate of \( 12\% \), and your \( \$200 \) investment would take around \( 42 \) years to hit \( \$28,000 \). A tempting offer, indeed!