Question 476060
For a 9% interest rate the Rule of 72 tells you that an investment will double in 8 years because 72/9 = 8.
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Since the original investment was $25,000 it will double to $50,000 in 8 years. Now you are starting with $50,000 and since the interest rate remains at 9%, the $50,000 will double to $100,000 in the next 8 years.  Up to this point your original investment of $25,000 has grown to be $100,000 in a total of 16 years.
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So at 16 years your $100,000 remains invested at 9%. It will again double in 8 more years. At that time the $100,000 doubles to $200,000 in 8 years. This added 8 year period makes the total investment period 24 years (16 + 8).
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In summary your original investment of $25,000 grows to $200,000 in 24 years if it is invested at 9% and is left untouched.
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A way of looking at this is that you double money every 8 years so that in 24 years you double, double again, and double one more time. This is 2*2*2 = 8 so that your original investment grows by 8 times (8 times $25,000 = $200,000).
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Hope this helps you to understand the Rule of 72.  It's more useful when the interest rates are higher than banks are paying at present.  If you deposit money at 1% it will take 72 years (72/1) to double your money, whereas in this problem you doubled your money every 8 years.