Questions: To plan for retirement, Latoya deposits 107 each month in an annuity that pays 7.2% interest, compounded monthly. Payments will be made at the end of each month. Find the total value of the annuity in 26 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, we will use the future value of an annuity formula. The formula for the future value of an ordinary annuity is:

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

where:

• \( P \) is the monthly deposit (\$107),
• \( r \) is the monthly interest rate (annual rate divided by 12),
• \( n \) is the total number of deposits (number of years times 12).

We will calculate the future value using these parameters.

Let:

• \( P = 107 \) (monthly deposit)
• \( r = \frac{0.072}{12} = 0.005999999999999999 \) (monthly interest rate)
• \( n = 26 \times 12 = 312 \) (total number of deposits)

Using the future value of an ordinary annuity formula:

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

Substituting the values:

\[ FV = 107 \times \frac{(1 + 0.005999999999999999)^{312} - 1}{0.005999999999999999} \]

Calculating the expression:

\[ FV = 107 \times \frac{(1.005999999999999999)^{312} - 1}{0.005999999999999999} \approx 97459.55303219537 \]

Rounding to the nearest cent gives:

\[ FV_{\text{rounded}} = 97459.55 \]

Final Answer