Question

After 16 years in an account with a 6.2% annual interest rate compounded continuously, an investment is worth a total of $58,226.31. What is the value of the principal investment? Round the answer to the nearest penny.

Answer 1

To find the value of the principal investment, we can use the formula for compound interest: A = P * e^(rt). In this case, the final amount is $58,226.31, the annual interest rate is 6.2%, and the time is 16 years.

Step-by-step explanation:

To find the value of the principal investment, we can use the formula for compound interest:

A = P * e^(rt)

Where:

• A = final amount
• P = principal investment
• e = Euler's number (approximately 2.71828)
• r = annual interest rate
• t = time in years

In this case, the final amount (A) is $58,226.31, the annual interest rate (r) is 6.2%, and the time (t) is 16 years. Plugging these values into the formula, we get:

$58,226.31 = P * e^(0.062 * 16)

Solving for P gives us:

P = $58,226.31 / e^(0.062 * 16)

Using a calculator to evaluate the exponential term, we find:

P ≈ $24,169.70