Question

adam invests $6,139 in an retirement account with a fixed annual interest rate compounded continuously. after 17 years the balance reaches $8,624.97. what is the interest rate of the account ?

Answer 1

The interest rate of the retirement account is approximately 4.1%.

Step-by-step explanation:

To find the interest rate of the retirement account, we can use the formula for compound interest. The formula is A = P * e^(rt), where A is the final balance, P is the initial investment, e is Euler's number (approximately 2.71828), r is the interest rate, and t is the time in years. We can plug in the given values to solve for the interest rate:

8624.97 = 6139 * e^(17r)

Solving for r, we divide both sides by 6139 and take the natural logarithm of both sides:

ln(8624.97/6139) = 17r

r = ln(8624.97/6139) / 17

Using a calculator, we find that r is approximately 0.041, or 4.1%.