You want to make an investment in a continuously compounding account earning 1.2% interest. How many years will it take for your investment to double in value? Round the logarithm value to the nearest thousandth. Round the answer to the nearest year.

I got 6 years, is this correct?

1 e^.012t = 2

take ln of both sides
ln e^.01t = ln2
.012t ln e = ln 2 , but ln e = 1
.12t = ln 2
t = ln2/.012 = 57.76 years
or 58 years to the nearest year.

To determine how many years it will take for an investment to double in value in a continuously compounding account, you can use the formula for continuous compound interest:

A = P * e^(rt)

Where:
A is the final amount (double the initial investment)
P is the principal (initial investment)
e is the mathematical constant approximately equal to 2.71828
r is the interest rate, expressed as a decimal (1.2% = 0.012)
t is the time in years we want to find

In this case, we want to find t, the number of years it will take for the investment to double. So we can rewrite the equation as:

2P = P * e^(0.012t)

Dividing both sides by P, we get:

2 = e^(0.012t)

To isolate t, we take the natural logarithm (ln) of both sides:

ln(2) = ln(e^(0.012t))

Since ln(e^x) = x, we can simplify further:

ln(2) = 0.012t

Now, we can solve for t by dividing both sides by 0.012:

t = ln(2) / 0.012

Using a calculator, we find that ln(2) ≈ 0.693. Hence, the calculation becomes:

t = 0.693 / 0.012

Simplifying, we get:

t ≈ 57.75

Rounding this value to the nearest thousandth gives approximately 57.750.

Therefore, it will take approximately 57.750 years for your investment to double in value in a continuously compounding account, rounded to the nearest year.

Hence, your initial estimate of 6 years is not correct.