Question

Kerry invests $400 in a bank account with a fixed annual intrest rate of 2.2% compound continuously when will the bank account triple

Answer 1

To find out when the bank account will triple, we can use the formula for compound interest. By substituting the values into the formula and solving for t, we find that it will take approximately 31.51 years for Kerry's bank account to triple.

Step-by-step explanation:

To find out when the bank account will triple, we can use the formula for compound interest:

A = P × e^(rt)

Where:

• A is the final amount
• P is the initial principal (the amount Kerry invested)
• r is the interest rate (2.2% as a decimal)
• t is the time in years

In this case, we want to find the value of t when the final amount is 3 times the initial principal:

3P = P × e^(0.022t)

Now, we can solve for t. First, divide both sides of the equation by P:

3 = e^(0.022t)

Take the natural logarithm of both sides to isolate t:

ln(3) = 0.022t

Finally, divide both sides of the equation by 0.022 to solve for t:

t = ln(3) / 0.022

Using a calculator, we can find that t is approximately 31.51 years.

Therefore, it will take approximately 31.51 years for Kerry's bank account to triple.