Questions: Lamar wants to save money to open a tutoring center. He buys an annuity with a yearly payment of 333 that pays 3.3% interest, compounded annually. Payments will be made at the end of each year. Find the total value of the annuity in 9 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 9 years, we can use the future value of an annuity formula. The formula for the future value of an annuity compounded annually is:

\[ FV = P \times \frac{(1 + r)^n - 1}{r} \]

where:

• \( FV \) is the future value of the annuity.
• \( P \) is the annual payment (\$333 in this case).
• \( r \) is the annual interest rate (3.3% or 0.033 as a decimal).
• \( n \) is the number of years (9 years).

We are given the following values for the annuity:

• Annual payment, \( P = 333 \)
• Annual interest rate, \( r = 0.033 \)
• Number of years, \( n = 9 \)

The future value of the annuity can be calculated using the formula:

\[ FV = P \times \frac{(1 + r)^n - 1}{r} \]

Substituting the given values into the formula:

\[ FV = 333 \times \frac{(1 + 0.033)^9 - 1}{0.033} \]

Calculating the expression:

\[ (1 + 0.033)^9 \approx 1.314624 \]

Thus,

\[ FV = 333 \times \frac{1.314624 - 1}{0.033} \approx 333 \times \frac{0.314624}{0.033} \approx 333 \times 9.528 \]

This results in:

\[ FV \approx 3424.6242 \]

Rounding the future value to the nearest cent gives:

\[ FV \approx 3424.62 \]

Final Answer