1. What is an Annuity?

An annuity is a series of equal payments made at regular intervals. Common examples include mortgage payments, car loans, retirement income payments, and lease agreements.

2. How the Annuity Formula Works

The present value of an ordinary annuity is calculated using:

Where:

• \( PV \) — Present value of the annuity
• \( PMT \) — Periodic payment amount
• \( r \) — Periodic interest rate (decimal)
• \( n \) — Number of payment periods

Explanation: The formula discounts each future payment back to present value terms and sums them all together.

3. Practical Applications

Details: This calculation helps determine how much a series of future payments is worth today, which is essential for loan amortization, retirement planning, and investment analysis.

4. Using the Calculator

Tips: Enter the periodic payment amount, interest rate per period (as a decimal), and number of periods. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between ordinary annuity and annuity due?
A: Ordinary annuity payments are made at the end of each period, while annuity due payments are made at the beginning. The formula differs slightly for annuity due.

Q2: How do I convert annual rate to periodic rate?
A: Divide the annual rate by the number of periods per year. For monthly payments, divide annual rate by 12.

Q3: Can this calculate loan payments?
A: Yes, this is the formula used to calculate loan payments when you know the present value (loan amount).

Q4: What if payments grow over time?
A: For growing annuities, a modified formula is needed that accounts for the growth rate.

Q5: How accurate is this calculation?
A: The formula provides the theoretical present value assuming constant payments and interest rate throughout the term.