Use the Rule of 70 to estimate how long it takes a dollar-sign 7000 investment to double if it grows at the annual rate 7 %. Compare with the actual doubling times.
Round your answers to three decimal places.
I found the estimated doubling time using Rule of 70 to be 10.
I am having an issue with finding the actual doubling time in years.
so you want:
7000(1.07^t) = 1400
1.07^t = 2
take log of both sides, and by the rules of logs
t log 1.07 = log 2
t = log2/log1.07 = appr 10.245 years
To find the actual doubling time in years, you can use the formula:
Doubling Time = ln(2) / ln(1 + r)
Here, "r" represents the annual growth rate expressed as a decimal. The natural logarithm (ln) is used to calculate the doubling time.
In this case, the annual growth rate is 7%, or 0.07 as a decimal. Let's calculate the actual doubling time:
Doubling Time = ln(2) / ln(1 + 0.07)
Using a calculator, you can find the natural logarithm of 2 (ln(2)) to be approximately 0.693. Similarly, the natural logarithm of (1 + 0.07) is approximately 0.067.
Doubling Time ≈ 0.693 / 0.067 ≈ 10.343
The actual doubling time is approximately 10.343 years, rounded to three decimal places.
Comparing this with the estimated doubling time using the Rule of 70 (which you correctly found to be 10), we can see that the estimated and actual doubling times are fairly close in this case.