# WHY FV IS NEGATIVE

## WHY FV IS NEGATIVE

Have you ever wondered why FV is negative while calculating the present value of a future sum? It can be a bit counterintuitive at first, but let's delve into the logic behind it and its implications.

### FV and Present Value: A Tale of Two Concepts

To understand why FV is negative, we need to first understand the concept of future value (FV) and present value.

• Future Value: FV refers to the value of a sum of money at a specific point in the future, taking into account the effect of interest. For example, if you invest \$100 today at an interest rate of 5%, the FV after one year would be \$105.

• Present Value: Present value (PV) is the current worth of a future sum of money, discounted by the effect of interest. In other words, it's the amount of money you would need to invest today to have that future sum at a specified point in time.

### The Intuition Behind FV's Negativity

When calculating the PV of a future sum, we use a negative sign for FV. This is because we're essentially converting a future value into its present equivalent. By multiplying a positive FV with a negative sign, we effectively "undo" the effect of interest and bring the future sum back to its present-day value.

### The Negative FV in Action

Let's take a practical example to illustrate how FV's negativity plays out. Suppose you're considering investing \$1,000 today at an annual interest rate of 10%. If you want to calculate the PV of your investment after one year, you would use the following formula:

``````PV = FV / (1 + r)^t
``````

Where:

• PV is the present value
• FV is the future value
• r is the annual interest rate
• t is the number of years

Plugging in the values, we get:

``````PV = 1000 / (1 + 0.1)^1
``````
``````PV = 1000 / 1.1
``````
``````PV = 909.09
``````

As you can see, the FV of \$1,000 after one year (assuming a 10% interest rate) is \$1,100. However, when we calculate the PV using the formula, we get a negative value of -\$909.09. This is because we're using a negative sign to convert the future value back to its present equivalent.

### Implications of Negative FV

The negative sign associated with FV has a few key implications:

• It signifies that the present value of a future sum is always less than its FV, assuming a positive interest rate. This is because interest acts as a "discounting" factor, reducing the worth of future money when expressed in today's terms.

• The magnitude of the negative FV increases as the interest rate or the time period increases. This is because a higher interest rate or a longer time period results in a greater discounting effect.

### Understanding Time Value of Money

The concept of negative FV is closely tied to the time value of money (TVM). TVM recognizes that money today is worth more than the same amount of money in the future due to the potential earning power of money over time. This is why we use discounting to convert future values into their present equivalents, resulting in a negative FV.

### Conclusion

The negative sign associated with FV is not an error or a quirk, but a fundamental aspect of calculating present values. It reflects the time value of money and helps us accurately determine the value of future sums in today's terms. By understanding why FV is negative, you can make more informed financial decisions and plan for the future effectively.

### Frequently Asked Questions

1. Q: Why is FV negative in present value calculations?

A: FV is negative in present value calculations because we're essentially converting a future value into its present equivalent. Multiplying a positive FV with a negative sign "undoes" the effect of interest and brings the future sum back to its present-day value.

1. Q: What does the magnitude of the negative FV tell us?

A: The magnitude of the negative FV tells us the present value of a future sum relative to its FV, considering the effect of interest rate and time period. A larger negative FV indicates a greater discount on the future value.

1. Q: How does FV's negativity relate to the time value of money?

A: FV's negativity is directly related to the time value of money (TVM). TVM recognizes that money today is worth more than the same amount in the future due to its potential earning power. By applying a negative sign to FV, we account for this time value and calculate the present value accordingly.

1. Q: Can FV ever be positive in present value calculations?

A: No, FV can never be positive in present value calculations. This is because the purpose of present value calculation is to convert a future value into its present equivalent, which always results in a negative value due to the discounting effect of interest.

1. Q: How does understanding FV's negativity help in financial decision-making?

A: Understanding FV's negativity helps investors and financial planners accurately assess the value of future cash flows and make informed investment decisions. It allows them to compare the present values of different investment options and choose the ones that offer the best returns.