Chapter 4: Interest Rates
The interest rate is an indication of how much is paid or collected for borrowed money. The borrower repays the amount he borrowed (principal) plus an additional sum (interest). To the borrower, interest is the cost of having money. To the lender, interest is his compensation for doing without money that he has lent to someone else. Said another way: Interest is the reason lenders are interested in lending.
Where money is put to productive use (in business), the interest rate has an impact on economic activity because to be profitable, a business must earn enough revenue to pay its expenses, and expenses include interest. Where interest rates are high, borrowing money to fund business operations is a losing proposition. Where they are low, more business operations can be profitably funded with borrowed money. Hence low interest rates mean growth and expansion of productive activity in general - more goods, more jobs, more profit.
Interest is generally expressed as an annual percentage rate to balance out the effect of time: A loan of $100 that costs $3 and must not be repaid for a year is said to have a 3% APR; but if the same loan must be repaid in six months, it is a 6% APR.
Present and Future Value
Various business calculations consider the value of money over time - particularly where profit margins are thin, recognizing that $100 today is worth more than $100 a year from now may make the difference between an operation running at a profit or at a loss. Both have to do with the interest rate.
- Present Value calculates what money received at a future date is worth today
- Future Value calculates what money paid out today would be worth at a future date
So when a company must invest $100 now to receive $105 on the same day next year, is it worthwhile? This depends on how much interest they could make in safer investments. If they could earn 3%, a $100 investment today would be worth $103 in a year, so an investment that would return $105 is attractive. If they could earn 6% and have $106 next year, then a return of $105 is not attractive. The difference of a few dollars seems paltry, but businesses invest hundreds of millions and the math works out the same.
The percentage rate used in calculations is highly arbitrary. Some firms consider any return above the rate of inflation to be acceptable, others set an arbitrary requirement for a higher return. This is fairly simplistic, as risk is also considered - so a firm may prefer a project with a lower return and less risk to one that has a higher return but greater risk.
(EN: Here the author spends some time presenting the equations for manually calculating present and future values - which I'm skipping.)
Compounding
There's a brief mention of compounding, which occurs when interest that is earned is not paid out but rolled back onto the principle. This is most common in investments. IF the simple interest rate on an investment is $5, the value at the end of a year is not $105.00 but $105.12- the additional twelve cents being the "interest on interest" earned as the monthly interest is rolled back into the total sum. Again, it's small change on small amounts, but can be quite significant when large sums are involved.
(EN: Again, the author explains manual calculation, which is a bit involved and largely moot to understanding the concept.)
Financial Calculations
The ability to calculate interest rate, present value, and future value are all that is needed to be able to calculate the price of any debt instrument - whether it is their own consumer debt or debt-based investment vehicles. This would not include equities, as their value is tied to the financial performance of a firm (rather than a contracted interest payment), which can vary according to many factors, though equities are always valued comparatively to debt-based investments.
It is most straightforward when an investment is being purchased when it is created and held until it matures: a bond sells at its face value and returns its stated interest rate. But when instruments are bought or sold between their creation and redemption, the amount paid is adjusted according to the current interest rates. For example, a 5% bond would sell at more than face value if the interest rate fell to 4% or less than its face value if the interest rate rose to 6% - this adjustment effectively means that the buyer will be getting the current interest rate regardless of the stated rate of the security.
It is for this reason that the term "yield" or "yield to maturity" is used in favor of interest rate, as the stated interest rate is not the same as the yield to the investor when the security is sold at any price other than face value.
There follows some mathematics to teach the reader how to manually perform various calculations to determine the price, yield, and return of debt securities.
Inflation and Interest Rates
Consumer price inflation influences interest rates because it influences the price that will be demanded to borrow money. Essentially, when prices rise (EN: or currency is debased) the value of money falls because more money is required to purchase the same goods in future. So those who lend money wish to protect their purchasing power by charging an interest rate that will at least preserve the value of their money against inflation, though it is more typical to demand an additional sum to compensate for risk and to provide profit.
There follows more mathematics to teach the reader to calculate the real return of an investment (in terms of its purchasing power) by adjusting the interest earned against the decay of inflation.