# Interest rates

As individuals, we face decisions every day that implicate saving money for a future use or borrowing money for consumption. If we want to make an investment, one important task for us is the analysis of transactions with present and future cash flows. When we place value on any asset, we are trying to determine the worth of a stream of future cash flows.
Money has** time value** which means that individuals prefer a given sum of money the earlier it is received.
Consider the following exchange: You pay $4,000 today and in return receive $3,500 today. Would you accept this arrangement? Not likely. But what if you received the $3,500 today and paid the $4,000 one year from now? Can these sums be considered comparable? Possibly, because a payment of $4,000 a year from now would probably be worth less to you than a payment of $4,000 today. It would be fair, therefore, to **discount** the $4,000 collected in one year; that means to cut its value based on the** time** that passes before the money is paid.
An** interest rate( r )** is a rate of return that reflects the relationship between differently dated cash flows.
If $3,500 today and $4,000 in one year are equivalent in value, then $4000 âˆ’ $3,500 = $500 is the required compensation for receiving $4,000 in one year rather than now. The interest rateâ€”the required compensation stated as a rate of returnâ€”is $500/$3,500 = 0.1428 or 14.28 percent.
Interest rates can be reflected in 3 ways:
1. Rates of return
2. Discount rates
3. Opportunity costs
The **opportunity cost** is the value that investors are willing to quit by choosing a particular investment over another. If the party who supplied the $3,500 had instead decided to spend it today, he would have forgone earning 14,28% on the money. So, 14,28% is the opportunity cost of current consumption over investing in this example.
From the perspective of an investor analyzing the market-determined interest rates we can see an interest rate r as being composed of a real risk-free interest rate plus a set of premiums that are required returns for bearing some different types of risk:
**r = Real risk-free interest rate + Inflation premium + Default risk premium + Maturity premium + Liquidity premium**
â€¢ The** real risk-free interest rate** is the interest rate for a completely risk-free security if no inflation is expected. In theory, the real risk-free rate echoes the time predilection of individuals for current versus future real expenditure.
â€¢ The **inflation premium** compensates investors for expected inflation and reflects the typical inflation rate expected over the maturity of the debt. The aggregate of the real risk-free interest rate and the inflation premium is the **nominal risk-free interest rate**.
â€¢ The **default risk premium** compensates investors for the risk that the borrower will fail to make a contractually agreed-upon payment on time and in the agreed-upon sum.
â€¢ If an investment needs to be converted to cash quickly, the** liquidity premium** compensates investors for the risk of loss relative to the investment's fair value.
â€¢ When maturity is extended, the **maturity premium** compensates investors for the increased exposure of the market value of debt to changes in market interest rates (holding all else equal).

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