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Please give me the correct answer with accurate calculation.

You must round to the nearest cent as​ needed!

To find the future value and total interest of the ordinary annuity, we will use the Future Value of $1.00 Ordinary Annuity table provided in the image.

Given dataTo find the future value and total interest of the ordinary annuity, we will use the Future Value of $1.00 Ordinary Annuity table provided in the image.

Given 
- Periodic payment ($ PMT $) = $2,300
- Annual interest rate ($ r $) = 8%
- Payment frequency = Quarterly (4 times a year)
- Number of years ($ n $) = 3

First, we need to determine the rate per period and the number of periods:
- Rate per period ($ i $) = Annual interest rate / Number of periods per year = 8% / 4 = 2% (or 0.02)
- Number of periods ($ t $) = Number of years × Number of periods per year = 3 × 4 = 12

From the table, find the future value factor for 12 periods at 2% per period. Referring to the provided table:
- The future value factor for 12 periods at 2% is 13.412.

Now, calculate the future value ($ FV $) using the formula:
\[ FV = PMT \times \text{Future value factor} \]
\[ FV = 2300 \times 13.412 \]
\[ FV = 30,847.60 \]

Next, calculate the total interest earned by subtracting the total amount of payments made from the future value:
\[ \text{Total interest} = FV - (PMT \times t) \]
\[ \text{Total interest} = 30,847.60 - (2300 \times 12) \]
\[ \text{Total interest} = 30,847.60 - 27,600 \]
\[ \text{Total interest} = 3,247.60 \]

Thus, the future value of the ordinary annuity is \$30,847.60, and the total interest earned is \$3,247.60.

Would you like more details or have any questions?

Here are 5 questions you can ask:
1. How do you determine the number of periods for an annuity?
2. Can you explain how to read the future value factor from the table?
3. What is the difference between an ordinary annuity and an annuity due?
4. How does the frequency of payments affect the future value of an annuity?
5. How do you calculate the present value of an annuity?

Tip: When working with annuities, ensure you accurately convert annual interest rates to the appropriate rate per period based on the payment frequency to avoid calculation errors.

Learn how to calculate the future value and total interest of an ordinary annuity with a detailed step-by-step solution. This problem covers key concepts in annuities, including periodic payments, interest rates, and payment frequencies. Suitable for professionals and students interested in financial mathematics.

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