Question

Christian invests a sum of money in a savings account with a fixed annual interest rate of 7% compounded continuously. After 5 years, the balance reaches $12,669.44. What was the amount of the initial investment? Round to two decimal places.

Answer 1

To find the initial investment, use the formula for compound interest. After 5 years, the balance reaches $12,669.44. The initial investment was approximately $8,927.43.

Step-by-step explanation:

To find the initial investment, we can use the formula for compound interest.

The formula for compound interest is:

A = P * e^(rt)

Where:

• A is the final amount
• P is the principal amount (initial investment)
• r is the interest rate per period
• t is the number of periods
• e is the base of the natural logarithm (approximately 2.71828)

In this case, we know that after 5 years the balance is $12,669.44 and the interest rate is 7% per year.

Using the formula, we can solve for P:

$12,669.44 = P * e^(0.07 * 5)

Simplifying the equation:

$12,669.44 = P * e^(0.35)

Dividing both sides by e^(0.35):

P = $12,669.44 / e^(0.35)

Using a calculator, we can find that e^(0.35) is approximately 1.4195.

Therefore:

P ≈ $12,669.44 / 1.4195 ≈ $8,927.43

So, the initial investment was approximately $8,927.43.