Find the PV of an ordinary annuity that pays $1,000 each of the next 4 years if the interest rate is 12%. Then find the FV of that same annuity. Round your answers to the nearest cent.

To calculate the present value (PV) and future value (FV) of an ordinary annuity, we can use standard formulas:

### Present Value (PV) of an Ordinary Annuity:
The formula for the present value of an ordinary annuity is:

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

Where:
- $ P $ is the payment amount ($1,000 in this case)
- $ r $ is the interest rate per period (12% or 0.12 per year)
- $ n $ is the number of periods (4 years)

### Future Value (FV) of an Ordinary Annuity:
The formula for the future value of an ordinary annuity is:

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

Let me now calculate the PV and FV of the annuity using these formulas.The present value (PV) of the ordinary annuity is **$3,037.35**, and the future value (FV) of the annuity is **$4,779.33**, both rounded to the nearest cent.

Would you like more details or have any other questions?

Here are some related questions:
1. How does the interest rate affect the PV and FV of an annuity?
2. What if the annuity were an annuity due instead of an ordinary annuity?
3. How would the results change if the interest rate were compounded monthly?
4. What happens to the FV if the number of periods is doubled?
5. How do you calculate the payment amount needed to reach a specific FV?

**Tip:** The present value of an annuity decreases as the interest rate increases because future payments become less valuable today.

Learn how to calculate the Present Value (PV) and Future Value (FV) of an ordinary annuity that pays $1,000 annually for 4 years with a 12% interest rate. This step-by-step guide covers key concepts like annuities, interest rates, and the time value of money. The final PV is $3,037.35 and the FV is $4,779.33, rounded to the nearest cent.

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