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Double your wealth. Kant Miss Company is promising its investors that it will double their money every 5 years. What annual rate is Kant Miss promising? Is this investment a good deal? If you invest \( \$ 450 \) now and Kant Miss is able to deliver on its promise, how long will it take your investment to reach \( \$ 35,000 \) ? Using the Rule of 72, what annual rate is Kant Miss promising? \( \square \% \) (Round to the neares_ whole percentage.)

Ask by Gibbs Grant. in the United States
Jan 22,2025

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Answer

Kant Miss is promising an annual rate of **14%**.

Solution

To determine the annual rate Kant Miss Company is promising using the **Rule of 72**, follow these steps: ### **Rule of 72 Overview** The Rule of 72 is a simple formula to estimate the number of years required to double an investment at a fixed annual rate of interest, or conversely, to estimate the annual rate needed to double an investment in a fixed number of years. \[ \text{Years to Double} \times \text{Annual Rate} \approx 72 \] ### **Given:** - **Doubling Period:** 5 years ### **Calculating the Annual Rate:** Using the Rule of 72: \[ \text{Annual Rate} = \frac{72}{\text{Years to Double}} = \frac{72}{5} = 14.4\% \] ### **Rounding:** - **Nearest Whole Percentage:** **14%** ### **Answer:** **14 %**

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Kant Miss Company claims it can double your money every 5 years. To find the annual rate, you can use the Rule of 72. Simply divide 72 by the number of years it takes to double (which is 5). So, \( 72 / 5 = 14.4\% \). Rounding to the nearest whole percentage, Kant Miss is promising an annual rate of approximately 14%. Now, let's calculate how long it will take for your initial investment of \( \$450 \) to grow to \( \$35,000 \). Given the approximate 14% annual interest, use the formula for compound interest: \( A = P(1 + r)^t \). Rearranging gives you \( t = \log(A/P) / \log(1 + r) \). Plugging in the numbers, you’ll find it takes about 25.5 years to reach your goal. So, buckle up for a long ride if Kant Miss delivers on its bold claim!

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