\( 1 \leftarrow \begin{array}{l}\text { Double your wealth. Kant Miss Company is promising its investors that it will double their money every } \\ 5 \text { years. What annual rate is Kant Miss promising? Is this investment a good deal? If you invest } \$ 450 \\ \text { now and Kant Miss is able to deliver on its promise, how long will it take your investment to reach } \\ \$ 35,000 \text { ? }\end{array} \) Is this investment a good deal? (Select the best response.) A. Yes. This investment is a good deal if you are earning higher than \( 14.87 \% \) rate of retum annually on your current investment. B. Yes. This investment is a good deal if you are eaming lower than \( 14.87 \% \) rate of return annually on your current investment. C. No. It is hard to tell whether this investment is a good deal or not.
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The Deep Dive
Let’s break down the investment promise! If Kant Miss Company promises to double your wealth every 5 years, we can calculate the annual rate using the Rule of 72. Essentially, you divide 72 by the number of years (5). This gives you an approximate annual interest rate of about 14.4%. So, if you can earn a higher return elsewhere, it might not be the best deal. Now, if you invest $450 and aim for $35,000, we need to see how long it’ll take at the promised doubling rate. Since your investment doubles every 5 years, let’s keep doubling: $450 → $900 → $1,800 → $3,600 → $7,200 → $14,400 → $28,800. You’ll need just about 25 years to hit that $35,000 mark at this rate – not too shabby in the long run!
