## Formula to Calculate Time Value of Money

The formula to calculate time value of money either discounts the future value of money to present value or compounds the present value of money to future value.

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

- FV = Future value of money,
- PV = Present value of money,
- i = Rate of interest or current yield on similar investment,
- t = Number of years and
- n = Number of compounding periods of interest per year

### Time Value of Money Calculation (Step by Step)

**Step 1:**Firstly, try to figure out the rate of interest or the rate of return expected from a similar kind of investment based on the market situation. Please note that the rate of interest mentioned here is not the effective rate of interest but the annualized rate of interest. It is denoted by*‘*’.**i****Step 2:**Now, the tenure of the investment in terms of number years has to be determined i.e. for how long the money is going to remain invested. The number of years is denoted by*‘*’.**t****Step 3:**Now, the number of compounding periods of interest per year has to be determined i.e. how many times in a year the interest will be charged. The interest compounding can be quarterly, half-yearly, annually, etc. The number of compounding periods of interest per year is denoted by*‘*’.**n****Step 4:**Finally, if the present value of money (PV) is available, then the future value of money (FV) after ‘t’ number of year can be calculated using the following formula as,

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

On the other hand, if the future value of money (FV) after ‘t’ number of the year is available, then the present value of money (PV) today can be calculated using the following formula as,

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

### Example

#### Example #1

Let us take an example of a sum of $100,000 today invested for two years at 12% rate of interest. Now let us calculate the future value of money if the compounding is done:

- Monthly
- Quarterly
- Half Yearly
- Annually

Given, Present value of money (PV) = $100,000 , i = 12% , t = 2 years

**#1 – Monthly Compounding**

Since monthly ,therefore n = 12

Future value of money (FV)= $100,000 * (1 + )^{12*2}

- FV = $126,973.46 ~
**$126,973**

**#2 – Quarterly Compounding**

Since quarterly, therefore n = 4

Future value of money (FV) = $100,000 * (1 + )^{4*2}

- FV= $126,677.01 ~ $
**126,677**

**#3 – Half Yearly Compounding**

Since half-yearly, therefore n = 2

Future value of money (FV) = $100,000 * (1 + )^{2*2}

- FV = $126,247.70 ~
**$126,248**

**#4 – Annual Compounding**

Since annually, therefore n = 1

Future value of money ( FV ) = $100,000 * (1 + )^{1*2}

- FV = $125,440.00 ~
**$125,440**

Therefore, the future value of money for various compounding periods will be –

The above example shows the calculation of the time value of money formula that depends not only on the rate of interest and the tenure of the investment but also on how many times the interest compounding happens in a year.

#### Example #2

Let us take the example of a sum of $100,000 to be received after two years and the discounting rate is 10%. Now let us calculate the present value today if the compounding is done.

- Monthly
- Quarterly
- Half-yearly
- Annually

Given, FV = $100,000 , i = 10% , t = 2 years

**#1 – Monthly Compounding**

Since monthly, therefore n = 12

Present value of money (PV) = $100,000 / (1 + )^{12*2}

- PV = $81,940.95 ~
**$81,941**

**#2 – ****Quarterly ****Compounding**

Since quarterly, therefore n = 4

Present value of money (PV) = $100,000 / (1 + )^{4*2}

- PV = $82,074.66 ~
**$82,075**

**#3 – ****Half Yearly ****Compounding**

Since half-yearly, therefore n = 2

Present value of money (PV) = $100,000 / (1 + )^{2*2}

- PV = $82,270.25 ~
**$82,270**

**#4 – ****Annual ****Compounding**

Since annually, therefore n = 1

Present value of money (PV)= $100,000 / (1 + )^{1*2}

- PV = $82,644.63 ~
**$82,645**

Therefore, the present value of money for various compounding periods will be –

### Relevance and Use

The understanding of the time value of money is very important because it deals with the concept that the money available at the present time is worth more than an equal amount in the future for its potential of earning interest. The basic idea behind the concept is that money can be invested to earn interest and as such the same amount of money is worth more today than it is later.

The concept of time value of money can also be seen in the parlance of inflation and purchasing power. Since inflation continuously erodes the value of money which eventually impacts the purchasing power negatively. Both inflation and purchasing power should be considered when money is invested today in order to calculate the real return on investment. In case the rate of inflation is higher than the rate of interest expected on the investment, then despite nominal growth, the money is worthless in the future which means loss of money in terms of purchasing power.

**Recommended Articles**

This has been a guide to Time Value of Money Formula. Here we learn how to calculate the time value of money using PV and FV formula along with practical examples and downloadable excel templates. You may learn more about Financial Analysis from the following articles –

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