Find the future value of an ordinary annuity of $2,000 paid quarterly for 4 years, if the interest rate is 7%, compounded quarterly. (Round your answer to the nearest cent.)

To find the future value of an ordinary annuity, we use the following formula:

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

Where:
- $FV$ = future value of the annuity
- $P$ = payment per period (in this case, $2,000)
- $r$ = interest rate per period
- $n$ = total number of payments

### Given dataTo find the future value of an ordinary annuity, we use the following formula:

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

Where:
- $FV$ = future value of the annuity
- $P$ = payment per period (in this case, $2,000)
- $r$ = interest rate per period
- $n$ = total number of payments

### Given 
- Payment ($P$) = $2,000
- Quarterly interest rate = 7% annually, so $r = \frac{7\%}{4} = 0.07/4 = 0.0175$ per quarter
- Time = 4 years, and payments are made quarterly, so $n = 4 \times 4 = 16$ periods

### Plugging values into the formula:

\[
FV = 2000 \times \frac{(1 + 0.0175)^{16} - 1}{0.0175}
\]

Now, let’s calculate this.The future value of the ordinary annuity is approximately **$36,563.35**.

Would you like further details or have any questions?

Here are some related questions to expand on the topic:
1. How would the future value change if the interest rate was compounded monthly instead of quarterly?
2. What would happen if the payments were made at the beginning of each period (annuity due)?
3. How does the future value differ if the payment amount changes each quarter?
4. Can you calculate the present value of the same annuity?
5. How does inflation affect the real value of the future amount?

**Tip:** For annuities, the compounding frequency significantly affects the future value—more frequent compounding leads to higher future values.

Find the future value of an ordinary annuity of $2,000 paid quarterly for 4 years, if the interest rate is 7%, compounded quarterly. (Round your answer to the nearest cent.)

Learn how to calculate the future value of an ordinary annuity with $2,000 quarterly payments for 4 years at an interest rate of 7%, compounded quarterly. This guide explains the key formula and concepts in the time value of money and annuities. Suitable for high school students in Grades 10-12.

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