2. A $5,000 investment has doubled to $10,000 in ten years. How much longer will it take for the investment to reach $15,000 if it continues to earn the same rate?

(1+r)^10 = 2.0

1+r = 2.0^0.1
r = 2.0^0.1 - 1

So, to grow by a factor of 1.5, will take

(1+r)^t = 1.5
2^.1t = 1.5
.1t = log1.5/log2
t = 10(log1.5/log2) = 5.85 years

Depending on when interest is posted, it could take up to 6 years to see the $15K

To solve this problem, we need to determine how many more years it will take for the investment to grow from $10,000 to $15,000.

First, let's calculate the rate of growth. The investment doubled from $5,000 to $10,000 in ten years. This means the growth rate is equal to:
(Ending Value - Starting Value) / Starting Value = ($10,000 - $5,000) / $5,000 = $5,000 / $5,000 = 1

Therefore, the growth rate is 1 or 100%.

Now, let's use the growth rate to find out how many more years it will take for the investment to reach $15,000.

The formula to calculate the future value of an investment is:
Future Value = Present Value * (1 + Growth Rate)^Number of Years

We want to find the number of years, so we can rearrange the formula as follows:
Number of Years = log(Future Value / Present Value) / log(1 + Growth Rate)

Substituting the given values:
Present Value = $10,000
Future Value = $15,000
Growth Rate = 1

Number of Years = log($15,000 / $10,000) / log(1 + 1)

Calculating it using a calculator:
Number of Years = log(1.5) / log(2)
Number of Years ≈ 0.176 / 0.301
Number of Years ≈ 0.584

Therefore, it will take approximately 0.584 years more for the investment to reach $15,000 if it continues to earn the same rate.