Time value of money

How to Calculate Time Value of Money (TVM) with a Financial Calculator

CFA FRM

I. Introduction

The Time Value of Money (TVM) is a fundamental financial principle that asserts that a certain amount of money today is worth more than the same amount in the future due to its potential earning capacity. This concept is crucial for both personal and business finance, influencing decisions about investments, loans, and savings.

Calculating the TVM accurately is key to making informed financial choices. Financial calculators are invaluable tools in this context, allowing individuals to perform TVM calculations efficiently and with ease. In this guide, we’ll explore the essential variables involved in TVM calculations and demonstrate how to use a financial calculator effectively.

II. Understanding the Five Key Variables

To effectively calculate the Time Value of Money, it is essential to understand the five key variables involved:

Present Value (PV): This is the current worth of a future sum of money or cash flow given a specified rate of return. PV helps determine how much a future sum of money is worth today.

Future Value (FV): This represents the value of an investment at a future date based on an assumed rate of growth. FV enables investors to project how much their money will grow over time.

Interest Rate (I/Y): The interest rate is the rate at which money grows over time, often expressed as an annual percentage rate (APR).

Number of Periods (N): This refers to the total number of compounding periods. It could be in years, months, or any other relevant time frame.

Payment (PMT): Periodic payments are the cash flows that occur at regular intervals. These could be deposits into a savings account or payments made on a loan.

III. Using a Financial Calculator for TVM Calculations

Using financial calculator requires familiarity with its keys and functions. Here’s how to use a financial calculator for TVM calculations systematically:

Open Online Financial Calculator: Let's first open BA II Plus Emulator Online as a reference:

BA II Plus Calculator

Identify the Calculator Keys:

  • PV, FV, I/Y, N, and PMT keys: These keys allow you to input the relevant variables for each calculation.
  • CPT (Compute) key: This key calculates the unknown variable when the other four are known.

Inputting the Variables:

  • Start by enter the known values. For instance, if you know the interest rate and number of periods, you’ll input these first before the unknown variable.
  • Press the appropriate variable key (e.g., PV, FV, etc.) on your financial calculator.

Solving for the Unknown Variable:

  • After inputting the known values, press the CPT then thekey for the variable you want to solve (e.g., if you want to know PV, press PV).
  • The financial calculator will compute and display the result.

IV. Examples of TVM Calculations

Example 1: Future Value Calculation

Suppose you invest $1,000 at an annual interest rate of 5% for 10 years. To find the future value:

  1. Enter 5 (interest rate), then press I/Y key, enter 10 press N key, and enter -1000 and press PV key (the investment is an outflow).
  2. Finally, press CPT and FV.
  3. The calculator shows that the future value is approximately $1,628.89.

Example 2: Present Value Calculation

If you want to know what a future cash flow of $2,000 in 5 years is worth today at a 3% interest rate:

  1. Enter 3 (interest rate), then press I/Y key, enter 5 press N key, and enter 2000 press FV key (as a future cash inflow).
  2. After that, press CPT and PV.
  3. The calculator will display that the present value is approximately $1,725.22.

Example 3: Future Value of Annuity Calculation

If you plan to deposit $500 annually for 15 years with an interest rate of 4%, you want to calculate the future value of this annuity:

  1. Enter 4 (interest rate), then press I/Y key, enter 15 press N key, and enter -500 press PMT key (payment is an outflow).
  2. Press CPT and FV.
  3. The calculator shows that the future value is approximately $10,011.79.

V. Tips and Troubleshooting

  • Understanding the Calculator Modes: Financial calculators may have modes that affect how payments are treated (e.g., “Begin” vs. “End”). Payments in “Begin” mode occur at the start of each period, while in “End” mode, payments occur at the end. Ensure that you’re in the correct mode for your calculations.
  • Common Errors: Double-check that you’ve input the correct signs for inflows and outflows (e.g., negative for expenses, positive for income). Verify that you are using the right keys for the variables.

VI. Conclusion

Understanding the Time Value of Money is crucial for effective financial decision-making. With the help of a financial calculator, you can streamline the process of calculating PV, FV, and other TVM-related figures. Practicing these calculations will enhance your financial literacy and empower you to make well-informed financial decisions for both personal and business purposes.

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