Page 24 - DMGT515_PERSONAL_FINANCIAL_PLANNING

Unit 2: Time Value of Money

By taking into consideration, the above illustration we get, Notes
A = P (1+i) n
A = 1000 (1 + .10) 3
A = 1,331

Notes Computation by this formula can also become very time consuming if the number
of years increase, say 10, 20 or more. In such cases to save upon the computational efforts,
Compound Value table* can be used. The table gives the compound value of ` 1, after ‘n’
years for a wide range of combination of ‘I’ and ‘n’.
For instance, the above illustration gives the compound value of ` 1 at 10% p.a. at the end
of 3 years as 1.331, hence, the compound value of ` 1000 will amount to :
1000 × 1.331 = ` 1331

Self Assessment

Fill in the blanks:
1. Simple interest (SI) = Po (I) (............................).

2. According to dividend capitalization approach dividend is paid .............................
3. An annuity is a stream of ............................ annual flows.
4. ............................ is repayment of loan over a period of time.
5. The nominal rate of interest and ............................ per year is equal.

2.3.1 Multiple Compounding Periods

Interest can be compounded, even more than once a year. For calculating the multiple value
above, logic can be extended. For instance, in case of Semi-annual compounding, interest is paid
twice a year but at half the annual rate. Similarly in case of quarterly compounding, interest rate
effectively is 1/4th of the annual rate and there are four quarter years.
Formula:

⎡ i ⎤ m×n
A = P1+ m ⎦ ⎥
⎢
⎣
Where,
A = Amount after a period.
P = Amount in the beginning of the period.

i = Interest rate.
m = Number of times per year compounding is made.
n = Number of years for which compounding is to be done.
Illustration 2

An amount of ` 1500.00 is deposited in a bank paying an annual interest rate of 4.3%, compounded
quarterly. Find the balance after 6 years.

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