What is meant by F, P, A, G in Compound Interest tables? Also Explain the terms F/P, P/F, A/F, A/P, F/A, P/A, A/G, and P/G in compound interest tables as shown in the following sample table from Engineering Economics analysis by Donald G Newman.
It would be very helpful if the answer is provided by a certain technique to help myself to keep it remembered (optional).
The correct answer and explanation is:
In compound interest tables, the letters F, P, A, and G represent different types of values and calculations related to interest rates and time periods. Understanding these terms is crucial in analyzing financial situations such as investment growth, loan payments, or savings accumulation over time.
F, P, A, G:
- F stands for Future Value: This is the value of an investment or loan at the end of a specified time period, considering compound interest.
- P stands for Present Value: This is the current value or amount of money before interest is applied.
- A stands for Annuity: An annuity is a series of equal payments made or received at regular intervals over time. The A in the table represents the amount of each periodic payment.
- G stands for Gradient: A gradient refers to a series of payments where each payment is larger than the last by a fixed amount. This is usually used to model situations where payments increase over time.
Relationships in Compound Interest Calculations:
- F/P: The Future Value (F) is calculated based on the Present Value (P). This ratio tells you how much a present value (P) will grow to at the end of a specific period (F) considering a given interest rate. It’s used to determine how much a present amount of money will be worth in the future.
- P/F: The Present Value (P) is calculated from a given Future Value (F). This tells you how much you would need to invest today to reach a specific future amount.
- A/F: The Annuity (A) is calculated based on the Future Value (F). This ratio shows how much each periodic payment would need to be if you want to reach a specific future value.
- A/P: The Annuity (A) is calculated from the Present Value (P). This ratio determines how much an individual payment should be if you have a certain present value to break down into regular payments.
- F/A: The Future Value (F) is calculated from the Annuity (A). This shows you the future value you will accumulate over time if you make regular payments (A).
- P/A: The Present Value (P) is calculated based on the Annuity (A). This is how you calculate how much you would need today to cover future periodic payments.
- A/G: The Annuity (A) is calculated based on a Gradient (G). This shows how much periodic payment will be needed when payments grow by a fixed amount.
- P/G: The Present Value (P) is calculated based on a Gradient (G). This calculates how much the initial amount is worth today when payments increase by a fixed amount over time.
Memory Aid Technique:
To help you remember these terms, visualize the following mnemonic using the word “F-A-P-G”:
- F – Future (Future value comes after the investment period, so it’s related to growth or accumulation.)
- A – Annuity (Periodic payments over time.)
- P – Present (The starting amount, before interest.)
- G – Gradient (Payment series that increases by a fixed amount each period.)
Now, for the ratios like F/P, you can think: “Future from Present”—what will your present amount turn into in the future? Similarly, for A/F, you can think: “Annuity from Future”—how much will you need to pay regularly to reach a future goal? Use these associations as building blocks to better recall the concepts.