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# Compounding

## The Time Value of Money

The principle of time value of money is the notion that the sooner a given amount of money is received the more valuable it is, due to its capacity to earn interest.

Central to the time value principle is the concept of interest rates. Interest rates are fixed in the marketplace and allow for equivalent relationships to be determined by forces of supply and demand. In an environment where the market-determined rate is 10%, it would be said that borrowing (or lending) Rs. 1,000 today is equivalent to paying back (or receiving) Rs. 1,100 a year from now.

### The Five Components of Interest Rates

- Real Risk-Free Rate
- Expected Inflation
- Default-Risk Premium
- Liquidity Premium
- Maturity Premium

### Time Value of Money Calculations

The ‘stated annual rate’ (quoted rate) is the interest rate on an investment if an institution were to pay interest only once a year.

The ‘effective annual yield’ (or EAR) represents the actual rate of return, reflecting all of the compounding periods during the year.

**Effective annual rate (EAR) = (1 + Periodic interest rate) m – 1**

Where,

m = number of compounding periods in one year

Periodic interest rate = (stated interest rate) / m

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