# VMC: What Is Time Value of Money?

The post was originally published here.

## Definition of Time Value of Money (TVM)

• Time value of money describes how the sum of money that you hold currently is worth more than the equivalent sum in the future.
• This is mainly because there is there are risks associated with receiving future value, but current cash in your hand doesn’t have those risks.
• Inflation, a rise in the general price level of goods and services, is one of those risks.
• Inflation erodes value. A meal at a restaurant today is likely to cost more in the future.
• A meal at a restaurant today is likely to cost more in the future.
• For example, \$100 could buy you more now or could earn more interest than it can in say five years.
• Present value is your calculation of what a sum of future money is worth today.

## What are the Factors that Influence the Time Value of Money?

• Compounding is when you earn interest on any investment you make.
• As time passes, you make more money because of the interest you earn.
• Compound interest is the earnings that you make based on the initial amount of investment and accumulated interest.
• On the other hand, simple interest is the interest you earn on the initial investment.
• Therefore when you add both the compound interest and the simple interest up, you get the total interest.

## What are the Effects of Compounding Periods on Future Value (FV)?

• The number of compounding periods can severely impact the calculations.
• The higher your frequency of compounding, the more interest you earn.
• For example, if you were earning interest every day, then you would have more money compared to if you were earning interest every month.
• Interest rates, therefore, aren’t the only important factor, compounding periods are just as important.

## Time Value of Money Formula

• Four variables are used in TVM calculation: Present value, future value, time, and an interest rate

FV = PV * (1 + (i/n)) ^ (n * t)
PV = FV / (1 + (i/n)) ^ (n * t)

## What is Present Value (PV)?

• When finding the present value, we discount the money from the future to the present to see how much it is worth today using an appropriate interest rate.
• We generally refer to the calculating of future cash flows as “discounting” because we are reducing those cash flows.

## Time Value of Money in Practice

• Say you had a spare \$100,000 lying around and you invested it at an interest rate of 10%.
• Now, using the future value formula, you would see that the \$100,000 would turn into \$110,000 in a year.
• The \$110,000 is calculated through the formula mentioned above -> \$100,000 (1 + 10%/1) ^ (1*1) = \$110,000
• However, if you wanted \$110,000 next year, but you could only earn an interest of 8% on the investment at this moment, then how much would you need right now to have \$110,000 next year?
• 110,000 / (1+ (8%/1) ^ (1 x 1) = \$101,851.85

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