part i - rule of 72\ndirections: using the rule of 72, determine either how many years it would take to…
part i - rule of 72\ndirections: using the rule of 72, determine either how many years it would take to double your investment, or what interest rate you would need to double your investment. you must show how you calculated you answer.\n1. how many years would it take to double your money with an investment earning 8% interest?\n2. how many years would it take to double your money with an investment earning 2% interest?\n3. how many years would it take to double your money with an investment earning 16%interest?\n4. how many years would it take to double your money with an investment earning 12% interest?\n5. what interest rate would you need on an investment to double your money in 4 years?\n6. what interest rate would you need on an investment to double your money in 20 years?\n7. what interest rate would you need on an investment to double your money in 13 years?
Answer
Explanation:
Step1: Recall the Rule of 72 formula
The Rule of 72 is $t=\frac{72}{r}$ (for finding time $t$ to double investment with interest rate $r$) and $r = \frac{72}{t}$ (for finding interest rate $r$ to double investment in time $t$), where $r$ is the interest rate percentage and $t$ is the number of years.
Step2: Solve question 1
Given $r = 8%$, using $t=\frac{72}{r}$, we have $t=\frac{72}{8}=9$ years.
Step3: Solve question 2
Given $r = 2%$, using $t=\frac{72}{r}$, we get $t=\frac{72}{2}=36$ years.
Step4: Solve question 3
Given $r = 16%$, using $t=\frac{72}{r}$, we obtain $t=\frac{72}{16}=4.5$ years.
Step5: Solve question 4
Given $r = 12%$, using $t=\frac{72}{r}$, we find $t=\frac{72}{12}=6$ years.
Step6: Solve question 5
Given $t = 4$ years, using $r=\frac{72}{t}$, we have $r=\frac{72}{4}=18%$.
Step7: Solve question 6
Given $t = 20$ years, using $r=\frac{72}{t}$, we get $r=\frac{72}{20}=3.6%$.
Step8: Solve question 7
Given $t = 13$ years, using $r=\frac{72}{t}$, we obtain $r=\frac{72}{13}\approx5.54%$.
Answer:
- 9 years
- 36 years
- 4.5 years
- 6 years
- 18%
- 3.6%
- Approximately 5.54%