Web Notes on TIME VALUE OF MONEY -COMPOUNDING TECHNIQUES for SEBI Grade A ( Officer) Exam Preparation

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TIME VALUE OF MONEY -COMPOUNDING TECHNIQUES

Finance (Phase -I & II) Time value of money
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    TIME VALUE OF MONEY -COMPOUNDING TECHNIQUES

    TIME VALUE OF MONEY

    Money that is available at the present time is worth more than the same amount in future, due to its potential earning capacity. Any amount of money is worth more, the sooner it is received, as money can earn interest. The rupee was worth more yesterday than today and rupee today is worth more than a rupee tomorrow. The rupee earned today has more value as compared to tomorrow because of :

    1. Inflationary economy,
    2. Uncertainty of future, and
    3. People always prefer to have money today so that they can invest such money in some profitable avenue and earn profit.

                  Future Money = Present Money (+) Interest

    Some important terms before discussing the practical aspects:

    1. Present Value(PV): this is current starting amount. This is money a person has in his hand at the present time, the initial investment for future.
    2. Future Value (FV): this is the ending amount at a point of time in the future. It is worth more than the present value, provided it is earning interest and growing over time.
    3. The number of Period (N): this is the time line for investment. It is usually measured in years but it can be any scale of time such as quarterly, monthly or even daily.
    4. Interest Rate (I): this is the growth rate of money over the lifetime of the investment. It is stated in a percentage value, such as 8%, 10% (0.08,0.10) etc.
    • There are two techniques in time value of money which are opposite to each other:
    1. Compounding,
    2. Discounting.

    Compound Value/Future Value:

    Compounding is a technique of converting present values to future values. It is the future value of present money invested at appropriate interest rate compounded annually or half yearly or so on.

    Compound value of single sum of money:

    CV =  P {1+r}n

    C.I. = CV(-) P

    Alternatively, using Compound Factor Table:

    C.V. =P (CFi.n Table),     

                         where CFi.n. is compound factor table

    Multiple Compounding:

    It means frequently compounding in a year. In case of multiple compounding, the effective rate increases.

    CV =  P {1+r/t}nxt

    Where t= number of times compounding in a year

                Or

    CV =  P {1+ER}n      

    Where ER is effective rate

    Effective Rate

    It is true rate of interest, taking into account compounding effect of frequent interest payments. If the interest payments and incomes are computed at end of each year, the interest rate is same, but interest may be computed more frequently, such as on monthly or semi-annual basis, effective rate will be different on basis of different time period. With the frequency of compounding, the effective rate of interest increases.

    Effective rate = {[1+r/t]t -1} x   100

    Compound value of series of unequal payments deposited at end of each year:

    CV =  P {1+r}n-1 +  P {1+r}n-2 +-----

    Compound value of series of unequal payments deposited at beginning of each year:

    CV =  P {1+r}n +  P {1+r}n-1 +    -----

    Annuity

    Series of payments of equal magnitude made at fixed intervals of time at same rate of interest like wages, pension, insurance premium, bond interest etc.

    Compound value of series of equal payments deposited at end of each year (Ordinary Annuity):

    CV of Ordinary Annuity=  P{  (1+r)n -1/r}

    Where, P is annual equal payment

    Alternatively, using Annuity Compound Factor Table:

    CV or Ordinary Annuity=P  (x) ACFi.n.

    Compound value of series of equal payments deposited at beginning of each year (Annuity Due):

    CV of Annuity Due= { P   (1+r)n -1   }      (1+r)

                                                          r

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