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What is Time Value of Money? How does it calculate ?


Time Value of Money: It is a concept that the value of money in our hand is more valuable today than the value we will receive in future. It is basically shows the effect of time on money value .For example if you lend Rs. 200, 000 to someone and the borrower has given two option to you that 1st he can pay you today , 2nd he will pay you after 5 years. In that case you prefer 1st option because there is no risk of default in payment of money and you can earn interest on that value if you invested somewhere and also there is no loss of purchasing power. With the help of time value of money we can take some decisions like investment, loan or lease. We can analyse which future investment option is best for today.

 Present Value: The current worth of future sum of money. It is also called present discounted value, higher the discounted values lower the present value.

Future Value: The value of money received at a specified date in future which is equivalent to the value of money receives today.

Interest: It is also called discount interest rate or growth rate. When future value is calculated interest is compounded which is known as growth rate and when present value is calculated interest is discounted which is known as discounted interest rate.

N: it denotes number of periods in future value or present value formula. The value of “n” will not be equal to the number of periods when interest is compounded monthly, quarterly and half yearly. For example Rs. 5000 invested for 2 years @ 5.6% interest compounded monthly. Then in that case n=2*12=24. Similarly in case of compounded quarterly and half yearly.

Formula to calculate future value:

  •  FVIF: With the help of Future Value Interest Factor (FVIF) table in which interest (i) and number of periods (n) are given. We can easily calculate future value.
  •  Mathematical Formulas: Through formulas we can calculate future value and present value. And the formula is:

                              FV=PV (1+i) n
Where,
PV= present value
FV= future value
i= interest rate
n= number of year

Formula to calculate Present Value:
  • PVIF: We can calculate present value with help of present value interest factor (PVIF) table in which number of periods and interest are given.  
  • Mathematical Formulas: we can use mathematical formulas to calculate present value and the formula is:

                           PV=FV/ (1+i) n

Formula to calculate number of periods (n):

           N = In (FV/PV)/In (1+i)

Formula to calculate interest rate (i):
          I = (FV/PV) 1/t -1

Example 1: If someone invested Rs. 10, 000 for 4 years with simple annual interest of 7% .Find out the future value?

Solution:
FV=PV (1+ (i *n))
=10, 000(1+ (0.07 * 4))
=10,000(1+ 0.28)
=10, 000 * 1.28
=12800

 Example 2: Ravi invested Rs.98000 @ 6% compounded quarterly for 5 years then how much amount he would get after 5 years?

Solution:
FV=PV (1+i) n
=98000(1+0.015) 20
=131991.79

Example 3: What is the present value of Rs.2, 30,000 to be received at the end of 3 years , assuming an interest rate of 8.4% compounded annually?

Solution:
PV=FV / (1+i) n
=230000/ (1+0.084) 3
=180567.76

Example 4: How long does it take for Rs. 5, 00,000 to grow into Rs.9, 25,000 @ 7.5% compounded half yearly?

Solution:
N =In (FV/PV)/In (1+i)
=In (925000/500000)/In (1+0.0375)
=In (1.85) /In (1.0375)
= 0.6151/0.0368
= 16.7
= 8 years

Example 5: What interest rate is implied if you borrow Rs. 4, 00,000 and repaid Rs.6, 50,000 in 4 years?

 Solution:
FV=PV (1+r) n
I= (FV/PV) 1/t-1
= (650000/400000) 1/4-1
=12.9%





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