Find the value of the ordinary annuity at the end of the indicated time period. The payment​ R, frequency of deposits m​ (which is the same as the frequency of​ compounding), annual interest rate​ r, and time period t are given.
amount ​$600​; quarterly​; 5.9​%; five years
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Part 1
The value of the ordinary annuity is ​$
  
enter your response here.
​(Round to the nearest cent as​ needed.)

To find the value of an ordinary annuity, we can use the formula for the future value $ A $ of an ordinary annuity:

\[
A = R \times \frac{(1 + \frac{r}{m})^{mt} - 1}{\frac{r}{m}}
\]

Where:
- $ R $ is the regular payment amount,
- $ r $ is the annual interest rate (in decimal form),
- $ m $ is the number of compounding periods per year,
- $ t $ is the number of years.

Given:
- $ R = 600 $,
- $ r = 5.9\% = 0.059 $,
- $ m = 4 $ (quarterly payments and compounding),
- $ t = 5 $ years.

Now, substitute these values into the formula:

\[
A = 600 \times \frac{(1 + \frac{0.059}{4})^{4 \times 5} - 1}{\frac{0.059}{4}}
\]

Let's break it down step by step:

1. Calculate $ \frac{r}{m} $:
   \[
   \frac{0.059}{4} = 0.01475
   \]

2. Add 1 to $ \frac{r}{m} $:
   \[
   1 + 0.01475 = 1.01475
   \]

3. Raise this result to the power of $ mt $ (which is $ 4 \times 5 = 20 $):
   \[
   1.01475^{20} = 1.337140
   \]

4. Subtract 1 from the result:
   \[
   1.337140 - 1 = 0.337140
   \]

5. Divide by $ \frac{r}{m} $:
   \[
   \frac{0.337140}{0.01475} = 22.85763
   \]

6. Multiply by $ R $ (the payment amount):
   \[
   600 \times 22.85763 = 13714.58
   \]

So, the value of the ordinary annuity at the end of five years is approximately **$13,714.58**.

Would you like more details or have any questions?

Here are 5 related questions:
1. How does increasing the frequency of deposits affect the future value of the annuity?
2. What would the value be if the interest rate was 6.5% instead of 5.9%?
3. How would the future value change if payments were made monthly instead of quarterly?
4. What is the formula for finding the present value of an ordinary annuity?
5. How is the future value formula modified if the interest rate compounds continuously?

**Tip:** The more frequently interest is compounded, the higher the future value of an annuity.

Find the value of the ordinary annuity at the end of the indicated time period. The payment​ R, frequency of deposits m​ (which is the same as the frequency of​ compounding), annual interest rate​ r, and time period t are given. amount ​$600​; quarterly​; 5.9​%; five years.

Find the future value of an ordinary annuity with quarterly $600 payments, an annual interest rate of 5.9%, compounded quarterly over 5 years. Learn step-by-step how to calculate using the annuity formula. Suitable for high school students in Grades 10-12.

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