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The Nature of Interest Rates

2 March, 2015 - 12:11

Consider a delightful problem of choice. Your Aunt Carmen offers to give you $10,000 now or $10,000 in one year. Which would you pick?

Most people would choose to take the payment now. One reason for that choice is that the average level of prices is likely to rise over the next year. The purchasing power of $10,000 today is thus greater than the purchasing power of $10,000 a year hence. There is also a question of whether you can count on receiving the payment. If you take it now, you have it. It is risky to wait a year; who knows what will happen?

Let us eliminate both of these problems. Suppose that you are confident that the average level of prices will not change during the year, and you are absolutely certain that if you choose to wait for the payment, you and it will both be available. Will you take the payment now or wait?

Chances are you would still want to take the payment now. Perhaps there are some things you would like to purchase with it, and you would like them sooner rather than later. Moreover, if you wait a year to get the payment, you will not be able to use it while you are waiting. If you take it now, you can choose to spend it now or wait.

Now suppose Aunt Carmen wants to induce you to wait and changes the terms of her gift. She offers you $10,000 now or $11,000 in one year. In effect, she is offering you a $1,000 bonus if you will wait a year. If you agree to wait a year to receive Aunt Carmen’s payment, you will be accepting her promise to provide funds instead of the funds themselves. Either will increase your wealth, which is the sum of all your assets less all your liabilities. Assets are anything you have that is of value; liabilities are obligations to make future payments. Both a $10,000 payment from Aunt Carmen now and her promise of $11,000 in a year are examples of assets. The alternative to holding wealth is to consume it.You could, for example, take Aunt Carmen’s $10,000 and spend it for a trip to Europe, thus reducing your wealth. By making a better offer—$11,000 instead of $10,000—Aunt Carmen is trying to induce you to accept an asset you will not be able to consume during the year.

The $1,000 bonus Aunt Carmen is offering if you will wait a year for her payment is interest. In general, interest is a payment made to people who agree to postpone their use of wealth. The interest rate represents the opportunity cost of using wealth today, expressed as a percentage of the amount of wealth whose use is postponed. Aunt Carmen is offering you $1,000 if you will pass up the $10,000 today. She is thus offering you an interest rate of 10% ($1,000 / $10,000 = 0.1 = 10% ).

Suppose you tell Aunt Carmen that, given the two options, you would still rather have the $10,000 today. She now offers you $11,500 if you will wait a year for the payment—an interest rate of 15% ($1,500 / $10,000 = 0.15 = 15% ). The more she pays for waiting, the higher the interest rate.

You are probably familiar with the role of interest rates in loans. In a loan, the borrower obtains a payment now in exchange for promising to repay the loan in the future. The lender thus must postpone his or her use of wealth until the time of repayment. To induce lenders to postpone their use of their wealth, borrowers offer interest. Borrowers are willing to pay interest because it allows them to acquire the sum now rather than having to wait for it. And lenders require interest payments to compensate them for postponing their own use of their wealth.