SOLUTION: This is the question: Rule of 72 (Refer to Exercise 87 in Section 1.3.) If an investment of $25,000 earns 9% annual interest, approximate the value of the investment after 24 y

Question 476060: This is the question: Rule of 72 (Refer to Exercise 87 in Section 1.3.)
If an investment of $25,000 earns 9% annual interest,
approximate the value of the investment after
24 years.
Rule of 72 Investors sometimes use the rule of 72
to determine the time required to double an investment.
If 72 is divided by the annual interest rate earned
on an investment, the result approximates the number
of years needed to double the investment. For example,
an investment earning 6% annual interest will double
in value approximately every 72 6 12 years.
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
For a 9% interest rate the Rule of 72 tells you that an investment will double in 8 years because 72/9 = 8.
.
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.
.
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).
.
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.
.
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).
.
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.
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