Questions: Raina wants to save money to open a tutoring center. She buys an annuity with a yearly payment of 399 that pays 3% interest, compounded annually. Payments will be made at the end of each year. Find the total value of the annuity in 8 years. Do not round any intermediate computations, and round your final answer to the nearest cent. If necessary, refer to the list of financial formulas.

Solution Steps

To find the total value of the annuity in 8 years, we can use the future value of an ordinary annuity formula: \[ FV = P \times \frac{(1 + r)^n - 1}{r} \] where:

• \( P \) is the yearly payment (\$399)
• \( r \) is the annual interest rate (3% or 0.03)
• \( n \) is the number of years (8)

We are given the following values:

• Yearly payment, \( P = 399 \)
• Annual interest rate, \( r = 0.03 \)
• Number of years, \( n = 8 \)

To find the total value of the annuity in 8 years, we use the future value of an ordinary annuity formula: \[ FV = P \times \frac{(1 + r)^n - 1}{r} \]

Substituting the given values into the formula, we get: \[ FV = 399 \times \frac{(1 + 0.03)^8 - 1}{0.03} \]

First, calculate \( (1 + 0.03)^8 \): \[ (1 + 0.03)^8 = 1.03^8 \approx 1.2668 \]

Next, calculate \( 1.2668 - 1 \): \[ 1.2668 - 1 = 0.2668 \]

Then, divide by the interest rate \( r \): \[ \frac{0.2668}{0.03} \approx 8.8933 \]

Finally, multiply by the yearly payment \( P \): \[ 399 \times 8.8933 \approx 3548.04 \]

Final Answer