## The Time Value of Money (Present Value and Future Value)

**Time Value of Money:**

We know that money deposited in saving account of bank or financial institutions, then depositor earn money monthly, quarterly or yearly other then deposited money at some pre mention ratio of interest. Depositor will receive his actual money plus the interest on money. Depositor can reinvest the money (that interest received from principal amount deposited) too and get more.

**Note:**

• Earning money known as interest.

• The time (interest receive for an example after one year) denoted as‘t’.

• Deposited money known as par value or face value or principal value (this terminology is used with fixed income securities like bonds) can be denoted as Present Value (PV)

• Pre mention ratio of interest known as Interest ratio denoted as ‘r’.

• Sum of earning interest and the principal value at the end of t time known as future value (FV).

• Interest receive on reinvestment of interest amount is known as compound interest.

**Methods of calculation of Interest:**

There are two methods available to find the interest in FV. One is the formula and 2nd is the Future value table.

**Example 1:
**

I deposited amount Rs. 1000 in bank and I will receive 5% interest after one year on my principal amount. What amount will I have (principal amount and interest) after one year? Simply we want to know the Future value of Rs.1000 including the interest receive from bank after one year.

The future value of my deposited amount is Rs. 1050. Where Rs. 1000 is my actual principal amount and Rs.50 is the interest amount receive at 5% after one year.

**Solution By formula:
**

By some mathematical calculation, we can find the Future value of money and formula is

FV = PV *(1+ r) t

Note (1+r) raise to power t.

Now from our example we know;

PV=1000

rv=0.05 (5%)

t= 1

FV=?

FV = 1000*(1+0.05)1 => 1000* 1.05 => 1050.

**Example 2:** let’s take another example in which we discuss the compound interest. Rs. 500000 invested by a person for 7 years and the interest ratio will receive at 12%. Find the future value and also find the compound interest. Remember interest receive on every one year at 12% and interest will reinvest at each year end.

**Solution by formula:
**

Now from our example we know;

PV=500000

r=0.12 (12%)

t= 7

FV=?

Compound interest=?

FV=500000 * (1+ 0.12)7 => 500000 * (1.12)7 => 1105350

As calculated FV includes;

• Principal value and its interest

• Interest on reinvestment of interest (received per year for principal value) which is compound interest.

Total interest earn= FV-principal value at start year => 1105350 – 500000 => 605350

As total interest earn includes;

• Normal interest

• Compound interest

Normal interest = principal amount * interest ratio * time => 500000*0.12*7 => 420000

Compound interest = Total interest earn – normal interest => 1105350 – 420000 => 185350.

Conclusion of example 2; we invest Rs. 500000 and receive normal interest Rs. 420000 and compound interest 185350.

**Example 3:** (Use of Time value of money by example)

We want to by a computer, we survey the computer market. We have two options given, which one is best for buyer.

Option 1: Pay Rs. 4000 today and Rs. 6000 after 2 years to buy a computer.

Option 2: pay all today get a credit of Rs. 500 (net price today is Rs. 9500).

Interest rate is 10%.

**Solution: **

Note: by using formula of future value, if any one amount is missing we can find from the respected given amounts. FV = PV*(1+r) t => PV = FV / (1+r) t

Option 1:

PV = 4000 + ( 6000 after 2 years)

PV = 4000 + ( find present value of 6000)

PV = 4000 + (PV = 6000/(1+r)t))

PV = 4000 + (6000/(1+0.10)2)

PV = 4000 + 4958.68 => 8958.68

Option 2: Rs. 9500 is PV as well as FV.

Answer option 1 is better for buyer.

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