Question

You invest $700 in an account that pays an interest rate of 6.5% compounded continuously calculate the balance of your account after 20 years round your answer to the nearest hundred

Answer 1

To calculate the balance of an account with continuous compounding interest, we can use the formula A = P * e^(rt), where A is the final account balance, P is the initial investment, e is Euler's number, r is the interest rate, and t is the time in years. In this case, the balance of the account after 20 years is approximately $2568.30.

Step-by-step explanation:

To calculate the balance of an account with continuous compounding interest, we can use the formula:

A = P * e^(rt)

Where:

• A is the final account balance
• P is the initial investment
• e is Euler's number (approximately 2.71828)
• r is the interest rate (in decimal form)
• t is the time in years

In this case, we have P = $700, r = 0.065 (6.5% as a decimal), and t = 20. Plugging in these values, we get:

A = 700 * e^(0.065 * 20) = 700 * e^1.3 ≈ 700 * 3.669 ≈ $2568.30