# Find the doubling time of an investment earning 7% interest if interest is compounded continuously is ____years.

Round to the nearest tenth of a year.

## e^(.07t) = 2

.07t lne = ln2
t = ln2/.07 = appr 9.9 years

## To find the doubling time of an investment earning 7% interest compounded continuously, you can use the formula for continuous compound interest:

Doubling time = ln(2) / (r),

where r is the interest rate as a decimal.

First, we need to convert the interest rate of 7% to a decimal: 7% = 0.07.

Now we can plug the values into the formula:

Doubling time = ln(2) / (0.07).

Calculating this gives us:

Doubling time ≈ 9.9 years.

Rounding to the nearest tenth, the doubling time is approximately 9.9 years.

## To find the doubling time of an investment with continuous compounding, we can use the formula:

Doubling Time = ln(2) / (r)

where ln denotes the natural logarithm function, and r represents the interest rate.

In this case, the interest rate is 7% or 0.07 (in decimal form).

Therefore, the doubling time can be calculated as follows:

Doubling Time = ln(2) / (0.07)

Now, let's calculate it step by step:

1. Find the natural logarithm of 2:
ln(2) ≈ 0.69314718056

2. Divide ln(2) by 0.07:
Doubling Time ≈ 0.69314718056 / 0.07

3. Evaluate the expression:
Doubling Time ≈ 9.902

Therefore, the doubling time of an investment earning 7% interest with continuous compounding is approximately 9.9 years (rounded to the nearest tenth of a year).