Question

Assume that you make a single, one-time investment of $2887 at time zero in an account that is expected to average 11.0% return per year for the next 30 years. how much do you expect to have in the account at the end of the 30 years? answer to 2 decimal places 11:13 pm 71

Answer 1

To determine the final amount after 30 years with an 11% annual return, we apply the compound interest formula, resulting in an expected amount of approximately $66,103.88.

Step-by-step explanation:

To calculate the expected amount in the account at the end of 30 years, we use the compound interest formula, which is \(A = P(1 + r/n)^{nt}\), where:

• P is the principal amount (the initial amount of money).
• r is the annual interest rate (decimal).
• n is the number of times that interest is compounded per year.
• t is the time the money is invested in years.

For a one-time investment that is compounded annually, \(n\) is equal to 1. Given that the initial investment (\(P\)) is \($2887\), the annual interest rate (\(r\)) is 11% or 0.11, and the time (\(t\)) is 30 years, the formula simplifies to:

\(A = 2887(1 + 0.11/1)^{1 \times 30}\)

Calculating this gives us:

\(A = 2887(1 + 0.11)^{30}\)

\(A = 2887(1.11)^{30}\)

\(A = 2887 \times 1.11^{30}\)

After computing, we get:

\(A = 2887 \times 22.8925\) (approximately)

\(A = 66103.88\)

So, you expect to have roughly \($66103.88\) in the account at the end of the 30 years.