You want to make an investment in a continuously compounding account earning 12.6% interest. How many years will it take for your investment to double in value? Round the natural log value to the nearest thousandth. Round the answer to the nearest year.
I got 10 years is it OK?
No, it is not ok.
2=e^.12t
ln2=.12t
.693=.12t
t=less than six years. Do the dang math, OK?
To determine how many years it will take for an investment to double in value in a continuously compounding account, we can use the formula:
t = ln(2) / (r * 0.01)
Where:
t = number of years
ln = natural logarithm
r = interest rate
In this case, the interest rate is 12.6%. We need to convert it to decimal form by dividing it by 100:
r = 12.6 / 100 = 0.126
Substituting the values into the formula:
t = ln(2) / (0.126)
Using a calculator, the natural logarithm of 2 is approximately 0.693. Let's plug in that value:
t = 0.693 / (0.126) = 5.5
Rounding to the nearest thousandth, we get:
t ≈ 5.476
To round the answer to the nearest year, we can round up if the decimal is 0.5 or greater, and round down if the decimal is less than 0.5. Therefore, the investment will take 6 years to double in value.
So, it seems that your answer of 10 years is incorrect. The correct answer is 6 years.