Question

Angela invested $15,000 in a savings account. If the interest rate is 4%, how much will be in the account in 10 years by compounding continuously? Round your answer to the nearest cent.

Answer 1

A = P * e^(rt)

Where:
A is the final amount in the account
P is the principal amount (initial investment)
e is Euler's number (approximately 2.71828)
r is the interest rate (in decimal form)
t is the time period (in years)

Let's plug in the values:

P = $15,000
r = 0.04 (4% as a decimal)
t = 10 years

A = 15000 * e^(0.04 * 10)

Now, let's calculate it:

A ≈ 15000 * 2.71828^(0.04 * 10)

A ≈ 15000 * 2.71828^0.4

A ≈ 15000 * 1.49182

A ≈ $22,377.30

So, after 10 years of continuous compounding at a 4% interest rate, there would be approximately $22,377.30 in Angela's savings account.