Final answer:
An investment will double in a number of years by dividing 72 by the interest rate, according to the rule of 72. The correct statement among the options given is that an investment of $4,500 will double in 8 years at a compound interest rate of 9%.
Step-by-step explanation:
The student is asking a mathematical question related to the rule of 72, which is a quick way to estimate the number of years required to double the invested money at a given annual compound interest rate. By dividing 72 by the interest rate, you get a rough estimate of the doubling time. Let's analyze each of the provided statements using this rule.
- An investment of $3,100 will double in 12 years at a compound interest rate of 5%.
- An investment of $9,000 will double in 10 years at a compound interest rate of 7%.
- An investment of $4,500 will double in 8 years at a compound interest rate of 9%.
- An investment of $3,000 will double in 4 years at a compound interest rate of 12%.
Using the rule of 72:
- 72 / 5% = 14.4 years, so the first statement is not true.
- 72 / 7% = approximately 10.29 years, so the second statement is approximately true.
- 72 / 9% = 8 years, so the third statement is true.
- 72 / 12% = 6 years, so the fourth statement is not true.
Therefore, the statement that is true is: An investment of $4,500 will double in 8 years at a compound interest rate of 9%.