This money (from the perspective of the entity taking the loan) is called interest. Interest is paid regularly at a particular rate for the use of money lent, or for delaying the repayment of a debt. If you take out a loan from a bank for $1,000 at an interest rate of 3%, you will need to pay the bank back $1,030 at the end of one year. So, a target decrease in the federal funds rate, ¯, shifts the MP curve to the right, which results in a decrease in the real interest rate and an increase in the inflation rate. IS curve edit An increase in the interest rate, from a leftward shift of the MP curve or higher level of inflation, produces lower total output, Q. Money Demand and Interest Rates: Economics of Demand 11:41 The Money Market: Money Supply and Money Demand Curves 6:24 Private Investment and Real Interest Rates 12:15. The real interest rate the borrower is paying is 1%. The real interest rate the bank is receiving is 1%. That means the purchasing power of the bank only increases by 1%. The real interest rate. Definition of Sinking Fund Formula. A sinking fund refers to a fund that is set up by the particular bond issuer in order to repurchase a definite portion of the bond issue or for the replenishment of a major asset or any other similar capital expenditure Capital Expenditure Capex or Capital Expenditure is the expense of the company's total purchases of assets during a given period determined.

Interest is the amount of money charged for the borrowing of money to compensate the lender for the lost opportunity cost of not having the money and to compensate the lender for the various risks of lending money, such as inflation risk and credit default risk. Indeed, the word risk is derived from the Tuscan word rischio, which the Tuscans considered the amount necessary to compensate for the lending of money. Usually, the amount of interest being charged is expressed as an interest rate, which is a percentage of the principal or balance per unit of time.

The concept of interest has a long history. Aristotle thought interest was evil, and according to the Koran, God condemned the charging of interest. The earliest known examples of interest were in ancient Mesopotamia, beginning in the 3^rd millennium B.C., when an interest rate of either 20% or 33% was charged depending on whether the loan was paid in silver or barley. However, the interest rate did not depend on the amount of time. [No doubt this simplified calculations that required using a sexagesimal (base 60) numbering system and pressing wedge-shaped (cuneiform) styles into wet clay tablets.]

Interest and Interest Rates

Interest rates are the rate of growth of money per unit of time. It is one of the most fundamental factors in investments, since so many financial assets depend on its value. It is used to determine the present and future value of money and of annuities. Many securities either pay interest or the payoff depends on the interest rate. Whether a business will invest in capital or issue securities depends on the interest rate. Hence, the interest rate allocates economic resources more efficiently. Governments control their economies by adjusting key interest rates through monetary and fiscal policies.

Interest is the cost of money, in the form of a loan, and like the price of virtually everything else, it is determined by supply and demand. In the United States and most other developed countries, the government has a major influence on the interest rate, adjusting it higher to cool the economy and adjusting it lower to stimulate it. The government can also increase the money supply by printing money, or through other monetary and fiscal policies. Another source of supply is the savings of people, businesses, and other organizations. The main demand for money is for loans by people and businesses. Demand can also be affected by the monetary policies of the government.

Charging interest on a loan is sometimes called usury, although in more recent times, it has acquired a negative connotation of excessively high or illegal interest rates being charged. In fact, when the usury rate is limited by law, the rate is called a usury ceiling. However, at least 2 states in the United States do not have usury limits: Delaware and South Dakota, which is why many credit card issuers are located in those states.

Nominal and Real Interest Rates

The nominal interest rate is the stated interest rate. If a bank pays 5% annually on a savings account, then 5% is the nominal interest rate. So if you deposit $100 for 1 year, you will receive $5 in interest. However, that $5 will probably be worth less at the end of the year than it would have been at the beginning. This is because inflation lowers the value of money. As goods, services, and assets, such as real estate, rise in price, it takes more money to buy them.

The real interest rate is the nominal rate of interest minus inflation, which can be expressed approximately by the following formula:

Real Interest Rate = Nominal Interest Rate – Inflation Rate = Growth of Purchasing Power.

For low rates of inflation, the above equation is fairly accurate. However, the actual growth of your purchasing power = the nominal interest rate divided by the inflation rate:

Formula Relating the Real Interest Rate,
Nominal Interest Rate, and Inflation Rate
1	+	R	=	1 + N1 + I
R = Real Interest Rate N = Nominal Interest Rate I = Inflation Rate

The above equation can be solved for the real interest rate.

Solving for the Real Interest Rate
(1 + R)(1 + I) = 1 + N	Multiply both sides by (1 + I).
1 + I + R + RI = 1 + N	Multiply out left-hand side to get terms.
R + RI = R(1 + I) = N - I	Subtract 1 and I from both sides.
R = (N – I)/(1 + I)	Divide both sides by 1 + I.

Real Interest Rate Formula
R	=	N - I1 + I
R = Real Interest Rate N = Nominal Interest Rate I = Inflation Rate

Because people invest to earn more purchasing power, they will only invest or lend money that pays more than the expected inflation rate. In this case, the nominal rate equals the real interest rate plus the expected inflation.

Nominal Interest Rate Equilibrium

Although there are many different interest rates, their differences result mainly from risk, but they all move up or down along with the prevailing rates. Thus, these rates can be abstracted as a single interest rate — the prevailing interest rate. Generally, as interest rates increase, saving increases and borrowing decreases, and vice versa. If investments pay higher interest, then more people, businesses, and other organizations will invest to earn more money. If interest rates decline, then the motivation to invest declines also, but borrowing increases, which increases demand for money. There is a point where supply equals demand — this is the observed or nominal interest rate.

Irving Fisher looked at interest rate equilibrium as the desire for a specific real rate of return plus the expected inflation rate:

Nominal Interest Rate = Real Interest Rate + Expected Inflation Rate.

If the expected inflation rate was high, then people would demand a higher nominal rate for their investments; for why would anyone invest if they did not expect a real return? Although no one can really know what future interest rates will be, the nominal interest rate can be somewhat indicative of the expected interest rates.

The Taxation of Nominal Interest Rates

Most earned interest, or any positive return from investments, is taxed. However, taxes currently apply to the nominal rate of return, not the real rate — thus, the tax rate on the real rate of return exceeds the published tax rate.

Real Rate of Return = Nominal Interest Rate × (1 – Your Tax Bracket) - Inflation Rate

Example: Calculating the Real Interest Rate after Taxes

If you earned 5% nominal interest on your money with 3% inflation, and you are in the 25% tax bracket, what is your real interest rate after taxes?

Solution:

Using the above formula:

Real Rate of Return = 5% × .75 - 3%. = .75%

As you can see from the above, if you are in a high tax bracket, you must earn significantly more than 5% to earn a decent real return. At the 35% bracket, given the above nominal interest rate and inflation rate, the real interest rate would be 0

Real Interest Rate On The Money Fund Equation