1. What are Annuity and Perpetuity?

An annuity is a series of equal payments made at regular intervals for a specified number of periods. A perpetuity is an annuity that continues forever. These concepts are fundamental in finance for valuing cash flows.

2. How Does the Calculator Work?

The calculator uses these financial formulas:

Where:

• \( PMT \) — Payment amount per period (USD)
• \( r \) — Interest rate per period (decimal)
• \( n \) — Number of periods (unitless)

Explanation: The annuity formula discounts future payments to present value, while the perpetuity formula assumes payments continue indefinitely.

3. Importance of Present Value Calculation

Details: Present value calculations are essential for comparing investment opportunities, valuing financial instruments, and making capital budgeting decisions.

4. Using the Calculator

Tips: Enter payment amount in USD, interest rate as decimal (e.g., 0.05 for 5%), and number of periods. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between annuity and perpetuity?
A: An annuity has a fixed number of payments, while a perpetuity continues indefinitely.

Q2: When would I use each formula?
A: Use annuity for loans, mortgages, or bonds with maturity. Use perpetuity for preferred stock or endowment valuations.

Q3: How does interest rate affect present value?
A: Higher rates decrease present value as future cash flows are discounted more heavily.

Q4: Can these formulas handle growing payments?
A: No, these are for constant payments. Growing annuities/perpetuities require modified formulas.

Q5: What if my interest rate is zero?
A: The annuity PV becomes PMT × n, and perpetuity PV is undefined (infinite).