1. What is the PERT Formula?

The PERT formula (A = Pe^rt) calculates the future value of an investment with continuous compounding. It's based on the mathematical constant e (approximately 2.71828) and provides the most aggressive growth scenario for investments.

2. How Does the Calculator Work?

The calculator uses the PERT formula:

Where:

• \( A \) — Final amount
• \( P \) — Principal investment
• \( e \) — Euler's number (~2.71828)
• \( r \) — Annual interest rate (in decimal form)
• \( t \) — Time in years

Explanation: The formula shows how money grows when interest is compounded continuously, rather than at discrete intervals.

3. Importance of Continuous Compounding

Details: Continuous compounding represents the theoretical limit of compounding frequency. While banks typically compound daily or monthly, continuous compounding provides the maximum possible growth and is used in many financial models.

4. Using the Calculator

Tips: Enter principal amount in dollars, interest rate as a decimal (e.g., 5% = 0.05), and time in years. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: How does continuous compounding differ from regular compounding?
A: Continuous compounding calculates interest at every possible moment, while regular compounding uses discrete periods (monthly, quarterly, etc.).

Q2: When is continuous compounding used in real life?
A: While rare in consumer banking, it's used in advanced financial models, certain types of bonds, and in theoretical economic calculations.

Q3: What's the difference between PERT and standard compound interest?
A: Standard compound interest uses (1 + r/n)^nt where n is compounding periods. PERT is the limit as n approaches infinity.

Q4: How accurate is this for real investments?
A: For typical bank accounts with daily compounding, the difference is minimal. For long-term investments, the difference becomes more significant.

Q5: Can this formula be used for depreciation?
A: Yes, with a negative rate it models continuous decay, useful for calculating depreciation of assets.