Question

You want to double your money. You put $6,000 in a bank account that pays 3% compounded continuously. How long will it take you to double your money? (Round to the nearest tenth years )

Answer 1

To double your money in an account that pays 3% interest compounded continuously, it would take approximately 23.1 years.

Step-by-step explanation:

To find out how long it will take to double your money, you can use the formula for compound interest:

A = P * e^(rt)

Where:

• A is the final amount
• P is the initial amount (in this case, $6,000)
• e is Euler's number, approximately 2.71828
• r is the interest rate (in this case, 3% or 0.03)
• t is the time (what we're trying to find)

In this case, we're trying to find when A is double the initial amount, so A = 2P:

2P = P * e^(0.03t)

Divide both sides by P:

2 = e^(0.03t)

Take the natural logarithm of both sides:

ln(2) = 0.03t

Divide both sides by 0.03:

t = ln(2) / 0.03

Using a calculator, you can find that t is approximately 23.1 years, rounded to the nearest tenth of a year.