Question

you deposit $4000 each year into an account earning 3% interest compounded annually. how much will you have in the account in 35 years? $ question help: video 1 video 2 message instructor submit question

Explanation:

Step1: Identify the formula for future value of an ordinary annuity

The formula for the future value \( FV \) of an ordinary annuity is \( FV = P \times \frac{(1 + r)^n - 1}{r} \), where \( P \) is the annual payment, \( r \) is the annual interest rate (in decimal), and \( n \) is the number of periods.

Step2: Convert the interest rate to decimal and identify values

The annual interest rate \( r = 3\% = 0.03 \), the annual payment \( P = 4000 \), and the number of years \( n = 35 \).

Step3: Substitute values into the formula

Substitute \( P = 4000 \), \( r = 0.03 \), and \( n = 35 \) into the formula:

$$ FV = 4000 \times \frac{(1 + 0.03)^{35} - 1}{0.03} $$

Step4: Calculate \( (1 + 0.03)^{35} \)

First, calculate \( (1.03)^{35} \). Using a calculator, \( (1.03)^{35} \approx 2.806793 \).

Step5: Calculate the numerator

Subtract 1 from the result: \( 2.806793 - 1 = 1.806793 \).

Step6: Calculate the fraction

Divide the numerator by \( r = 0.03 \): \( \frac{1.806793}{0.03} \approx 60.22643 \).

Step7: Calculate the future value

Multiply by \( P = 4000 \): \( FV = 4000 \times 60.22643 \approx 240905.72 \).

Answer:

\( \$240905.72 \) (rounded to the nearest cent)