Interest is the amount of funds paid to a lender in addition to the funds borrowed. Interest rate is the fixed or variable amount payable per unit time, given as a percentage or fraction of the principal and therefore determines the exact funds paid in a given period of time. The borrower can be an individual, company, country or a banking institution. There are different sub-types of interest rates depending on the individuals and circumstances involved when determining the interest rate, however the main ones are; real interest rates and nominal or market rates (Dewey 11). Market rates are set through negations between buyer and seller in dealer markets that trade corporate bonds and treasury and these rates are subject to fluctuations on a daily basis. Administered or real rates are set up by establishments and include prime rate which is the interest rate charged by banks to their best clients, and discount rate, which is the interest rate at which banks pay back loans to the central bank or federal reserve. Central banks are primarily responsible for setting the interest rate but this does not entirely affect the interest rates set by lending institutions, since each institution has different risks involved in lending (Rogers 32). Interest rates are used to determine the interest to be received on a bank loan or account deposit. There are various types of interests, but in this paper we will be looking at the main ones which are; simple interest and compound interest.
Simple interest is the most basic type of interest and the easiest to calculate and understand. The Formula for simple interest is:
- I=P x R x T, or interest=Principal x Rate x Time period.
For example, if an investor invests $100 at the rate of 10 percent for one year, then the interest will be $10, or 100(p) x 0.1(r) x 1(t). This type of interest calculation is the basis of other more intricate types of interests used by financial institutions.
Annual percentage yield is commonly used to arrive at the interest for funds in a savings account. Annual percentage yield is therefore the amount of interest an account holder will earn over a period of twelve months, and unlike simple interest, annual percentage yield integrates compound interest to arrive at the total interest.
Therefore, if for example an account holder had $100 in their savings account at the end of the first month, they would earn $0.17 (0.1667% x 100). The following month, they will earn 0.1667% on the full amount which is $100.17 that they now have in their savings account. This mean that every month they would consequently receive interest on a constant increasing balance at the bank, and this will result in more than 4% interest over the course of that year (Rasche 89).
Companies that offer credit cards normally calculate their interest on a daily basis and this is meant to maximize their profits, given that the faster/more frequently they calculate the interest, the more money they make. Another form of interest calculation popular with credit card companies to arrive at higher interest is the use of average daily balance. For instance, if one has a $500 balance on their credit card on the first day of the 30-day billing cycle and they pay it off on the second day, your average daily balance for that billing cycle would be $16.67 or $500/30. If they wait until the 29th day of the billing cycle to pay it off, your average daily balance would be $483, or 14,500/30.
Amortized interest is another type of interest that is paid above loans like mortgage or car loans. Unlike simple or compound interest, the payments on this type of loan are calculated so that a person pays all of the interest due each month in addition to a small amount of the principal (Rogers 54).
For example, if one borrowed $500 at 2%, after one month you would owe the bank $500.83 obtained by calculating;
- 2%/12 months = 0.1667%, thus, 0.1667% x 500=$0.83.
If they paid the bank $100, they would then owe the bank $400.83, so the following month the interest would only be $0.67. The payment on an amortized loan is calculated so that the loan is paid off in just the right size increments to equal the desired number of payments. These interest calculations are common in arriving at the total amount money due on a monthly basis on long term loans covering buildings, houses and cars.
Interest rate determinants
There are several factors that are considered in modern economies before a specific interest rate is arrived at. These factors include:
If a country’s economy is healthy, the interest rate tends to rise. This healthy economy stimulates development and savings by job creation which is propelled through financial institutions like banks. Increase in development means increase in borrowing which gives that country’s currency greater demand. An increase in savings also means the availability of more funds for the banks. Improved economic conditions also amplify investment into commercial and personal ventures. Individuals tend to buy more expensive items like vehicles and houses and use credit facilities like credit cards while companies seek to expand their business venture to new markets.
More funds are needed for these ventures and hence greater demand for the particular currency. Interest rate is therefore correlated to the performance of an economy (Dewey 29). Looking at the last decade, early 2000 saw economic growth which is indicated by rising interest rates. Early 2001, the economy crumbled partly due to the 9/11 terrorist attack and the subsequent wars that followed. Mid 2004 attracted growth, which was experienced till late 2007 when the recession begun. The interest rates can therefore be useful in analysing economic data.
Loans given out by financial institutions usually have a fixed interest rate which is stipulated in the contract. Inflation usually devalues a given currency and so indicators of an impending inflation will consequently increase the interest rates. This is because banks will be hesitant to give out loans at the prevailing interest rate if they suspect that after a given period that amount of funds will be of lesser value in terms of purchasing power. To curb this, banks will increase the interest rate to a value they project will be of similar worth as the current one in a future inflated market.
This is similar to inflation but here the rise in prices is too high and happens within a relatively short period of time when the currency of a country loses value. Hyperinflation is usually reported on a monthly basis characterised by a fifty percent monthly inflation rate contrary to inflation which is reported only once a year. It is identified by observing market and human economic activities and some of the indicators of a hyperinflation are; the general populace will keep their wealth in goods, commodity, foreign currency or contact form, avoiding the domestic currency. Widespread fear that the Local currency is losing value will cause rapid disposing of it through bulk purchase of non-monetary assets. Domestic currency is valued in the form of a more stable foreign currency and the country can adapt by the valuation of the foreign currency as the benchmark for financial assessment. The nominal interest rate rises due to increased inflation rate and the risk involved in repaying loans in such conditions. Normally, a price index is formed based on the total income and expenses on a national scale and a three year mean period in a hyper inflated market will give the rate of inflation as roughly one hundred percent. Such conditions will inevitably affect the interest rate leading to abnormal figures when calculated (Dewey 152).
Foreign investors interested in a particular market for example the United States greatly influence the interest rate. When interest rates are high foreign investors may intervene and lower the rates by lending money to the U.S, reducing the pressure on the domestic sources of money. Presence of numerous international investors in a country therefore lowers the interest rate but increases the demand for that particular currency.
The U.S dollar has for a long time been the currency of choice for international trade. For this reason, sudden fluctuations in the dollar’s exchange rate can adversely affect weaker counter currencies. A shift in the dollar’s interest rate will affect the dollar’s demand and supply and therefore some currencies will have their interest rates revised especially countries that depend on international trade like export or import to support their economy.
Most capitalist nations have financial structures in place that hold the economy together and keep money flowing through it. Changes or Collapse of such structures is most likely prone to affect the interest rates, like it happened during the recession. It begun with less consumer spending which led to less demand for goods and services and eventually job cuts due to low sales. The epic of it was multi-national companies which support thousands of jobs and numerous shareholders were threatened with collapse. The federal government in the U.S had to intervene to bail out most of these companies and save the depositors from financial ruin at the expense of the federal budget deficit. There were also stimulus packages and the Federal Reserve opened bank reserves all aimed at increasing the supply of money in the market and this made the interest rates low. Financial structures are therefore a powerful interest rate determinant, albeit they rarely change or collapse (Rogers 61).
One other factors that affect interest rates is political stability, political stability is one of the fundamental factors that inadvertently determine the interest rate. Political instability generally pushes away foreign investors, causes an economic go-slow or even a civil war. Once such an occurrence unfolds, the currency of that nation becomes more or less devalued and of low demand. Financial institutions lending out funds will place a high interest rates to cushion against an unpredictable market caused by political tides. Once stability is restored and an economy revived, interest rates are lowered to attract domestic investment to boost the economy.
Also known as Fed, this institution determines the money that will be available for lending in the U.S and it is also responsible for setting the interest rate for the dollar. Established in December 23, 1913, the Federal Reserve System begun its operations in 1914 after the then president of the United States, President Woodrow Wilson passed the Federal Reserve Act through the senate and entrenched it into law. It was the brain child of Glass-Willis, who proposed for a decentralized banking system that was immune to collapse (Eatwell 23). By monitoring and intervening where it is necessary, Fed makes regular adjustment to the interest rate based on the economy or irregularities in the financial market. In a healthy economy, the Fed will raise short term interest rates to avoid a rapid economic growth which is the precursor for inflation. Inflation will be brought about by the presence of excess funds in the economy that need goods and services which in their normal supply cannot satisfy the needs of the excess funds. The goods and services will have to increase their prices to filter out demand leading to inflation. High interest rates exposes the borrower to increased borrowing costs and therefore less likely to invest in a flooded market. Short term rates are lowered by the Fed if there are indications of a contracting economy, making it cheaper to borrow and invest, and stimulating economic growth so as to avoid plunging into a recession (Rasche 59).
Economic studies of interest rates have attracted several theories that seek to determine how the interest rate can best be standardized. Various economic scholars from different time periods came up with different laudable theories to determine the interest rate. For instance, Adam Smith came up with the classical theory of interest which suggested that the interest rate was an economic force that primarily balanced the pull of investment with that of savings. Marxist economic theory was nurtured in a socialist economy and argued that interest was a suppressive economic manoeuvre seeking to benefit the capitalist class since no service was render to warrant interest. Eugen Böhm-Bawerk’s productivity theory was a revised edition of the Nassau senior’s Abstinence theory and the productivity theory expounded on interest as the determining component on whether to save or consume funds. High interest rates were therefore responsible for increased savings since saving money in a bank account instead of using the money for consumption of goods and services increased the earnings of the account holder. Irving Fisher expanded the productivity theory by considering the will of individuals to forfeit their present gains for greater future gains as an important factor in investment decisions (McCallum 57).
Fisher effect equation
This equation was created by Irving Fisher and it was formulated to show the relationship between price and the supply of money. It basically was aimed at proving that if a country’s expected inflation rate rises, the interest rate will also ultimately rise in similar measure. The Fisher effect therefore argues that the nominal interest rate is primarily determined by expected inflation. The basic formula is:
MV = PQ
- M is the amount of money in supply
- V is the number of times a monetary unit is spent on finished goods and services per annum, or simply the velocity of M money per year
- P is the price level, which is the average of the prices of all goods and services
- Q is the physical quantity of final outputs of goods and services in one year
- PQ is therefore the total money spent in an economy in one year
This equation derives that; since V is more or less a constant, increase in M will stimulate consumer spending thus an increase in total money spent in a year or PQ. A short term increase of M will inevitably lead to an increase in price P, assuming that the physical quantity Q is not likely to increase in the short term. Therefore, a conclusion can be drawn based on the equation stating that short time increases of money supply will inevitable increase the price of goods and services P in the near future.
Assigning arbitrary numbers to M, V, P and Q we will have:
Therefore, MV=PQ=1000 if over the short term M was to be increased by 50% which is 100 hence M=300 V being a constant and Q unchangeable over the short term, then MV=PQ (300) (5) = (P) (4) 1500=P4
To get the percentage increase of P, then it would be:
- (375-250)/250 X 100
- 125/250 X100
- 0.5 X100
The percentage increase on the price level P is 50%, influenced by 50% increase in money in circulation M.
A simpler version of the Fisher equation is:
n = i + r
- n-is the nominal or market interest rate
- i- is the inflation rate
- r- is the real interest rate
It is then very easy to calculate the market interest rate and this is by simple addition. Assuming the inflation rate is at 4% and the real rate which usually ranges between 2-3% is at 2%. The market interest rate will therefore be:
4 + 2 = 6 therefore, the nominal interest rate would be 6%.
Fisher effect equation in determining interest rate
The equation (n = i + r), is used in determining the interest rate since it is used to calculate the nominal rate from the inflation rate and the real rate. If the inflation rate and another interest rate have known values, then the nominal and the real interest rates can be calculated. Nominal interest rate can be acquired by adding the inflation rate to the real rate and this gives you the interest rate that you will find most financial institutions lending out with. The real interest rate is determined by the central banks or the Federal Reserve and this too can be predicted if the inflation rate and the current market interest rate are available. From the Fisher formula, the simples approach would be to subtract the inflation rate from the market interest rate.
r = n – i
Fisher effect equation in determining exchange rate
This is found under Uncovered Interest Parity, where the international Fisher effect states that the difference in nominal interest rates between two countries also affects the nominal exchange rate of their currencies, with the currency with lower nominal interest rate increasing in value (McCallum 47). It maintains that real interest rates should be the same in all countries in the world and that money should flow internationally.
The spot exchange rate on the Euro based against the dollar is USD1.6452 on the Euro. The U.S has a nominal interest rate of 4% and the Euro zone has an interest rate of 7%. According to Fisher effect equation, it is possible to predict the spot exchange rate for the pair one year later by comparing nominal interest rates. This is done by multiplying the current spot exchange rate with the U.S nominal interest rate, then dividing all with the Euro zone nominal inflation rate.
[Sr X (1+Lr)]/ (1+Hr)
- Sr is the current spot exchange rate
- Lr is the nominal interest rate of the currency with the lower nominal rate
- Hr is the nominal interest rate of the currency with the higher nominal rate
[1.6452 X (1+0.04)]/ (1+0.07)
(1.6452 X1.04)/ 1.07
This would then be considered to be the value of the pair twelve months from now.
Fisher’s equation in determining inflation rate
Inflation rate can be obtained using the first and second formula. The first formula MV=PQ is very effective especially when there has been a short term increase in the circulation of funds in an economy. According to this formula, a short term injection of funds in the economy at a given rate will cause inflation of the economy in the near future of a similar rate as the monetary influx (Meltzer 15). The second equation, n=i+r, will clearly retrieve the inflation rate, as long as the market interest rate (n) and the real interest rate (r) are known. From the equation, the inflation rate will therefore be given as;
i = n – r
Inflation rate can also be calculated from consumer price index (CPI) data using the formula:
i = [CPI (this year) – CPI (last year)] / CPI (last year).
The Federal Reserve and money supply
Established in 1913, the Fed is made up of both members of the public and private sector and this constitutes its leverage in being able to determine the best credit and interest rate in the prevailing market. It has a unique administrative structure which is headed by The Board of Governors also known as the Federal Reserve Board and it is located in Washington, D.C. The Board is the national component of the Federal Reserve System.
The Federal Reserve System regulates the monetary supply in the United States by monitoring and regulating the amount of loans made by commercial banks. The money that commercial banks are able to avail in form of loans is the money found in the banks’ excess reserves and this is where the Federal Reserve is able to control and pose influence over the excess reserves. By so doing, the Federal Reserve gains the ultimate advantage to control loans, monitor checkable deposits and influence the money supply (Schwartz 31). The Federal Reserve has a variety of ways by which it can change the supply of money through commercial banks, like the buying and selling of bonds and treasury, also known as open market activities, lending to banks and various financial institutions at a discount rate and altering the statutory reserve ratio to coincide with the current economic conditions.
The Fed determines the amount of credit to be availed to the banks; it monitors the U.S currency and takes appropriate measures to ensure the stability of the dollar, both in the local and international market (Dewey 39). The Federal Reserve is also responsible for setting the interest rates that will determine the performance of the economy. Its main role is to control the accounts holding the existing stock of currency. However, it is within its mandate to effectively monitor and manage the flow of money in the U.S economy to avert inflation and or recession. There are certain situations that call for tightening money supply while others require the Fed to ease monetary supply. The following are some of the ways the Fed can ease and tighten money supply depending on prevailing circumstances.
Ways Federal Reserve can tighten money supplies
In the event of a fast growing economy, the Federal Reserve may be required to reduce the flow of currency or the amount of liquidity to avoid the occurrence of inflation. Inflation emerges when an economy is growing too fast and available goods and service providers are not able to satisfy all willing buyers (Eatwell 78). Consequently due to high demand and low supply, goods and services in such an economy end up being overpriced, setting inflation into motion. There are a few things that the Federal Reserve can do to avoid inflation and this is mostly by cutting down on the money entering the U.S economy.
The Federal Reserve can increase discount rates on the funds it lends to depository institutions so as to reduce on the number of borrowers who are interested in taking out loans. High rates discourage individuals who are mostly borrowing for consumption and at the same time dissuade investors from diverting borrowed loans to finance less viable ventures (Rogers 14). This in turn changes the market perception of the economy, since an overly buoyant economy will sooner or later allow demand to exceed current output capacity.
It is also possible for the Federal Reserve to purchase U.S treasury securities through open market transactions then pay for the treasury securities by writing self drawn cheques. In so doing, the Fed increases its reserves while at the same time reduces the supply of money into the economy.
Reserve spaces available at the Federal Reserve should be limited and competitive. This will ensure that banks drawing out from their reserves stand to lose that reserve to another bank which may increase deposits in the same reserve and therefore the withdrawing bank is less likely to receive substantial loans (Schwartz 23). This will encourage a saving culture in the banking sector and at the same time minimise the money going into circulation.
In addition, the Federal Reserve can reduce the flow of excess currency by holding a percentage of its reserves as foreign currency, foreign contracts and commodities. This reduces the amount of money available for lending and at the same time increases investment yield which can be attained by selling the foreign currency or commodities reserve after a given period of time. Foreign currencies can be of profitable interest if the Federal Reserve is to consider interest rates differentials before investing in a particular currency.
Ways the Federal Reserve can ease money supply
There are certain circumstances in an economy which may lead to an unexpected or speedy reduction of money in the same economy. Deflation is the sudden shrinking of a buoyant economy which leads to a fall in prices of goods and services specifically due to lower flow of money in the economy (Meltzer 98). A recession is also attributed to low supply of money, but it is caused by overly conservative consumers who are not willing or are not in a position to spend as much money that can sustain the growth of the economy. In such situations, the Federal Reserve will normally intervene to save the economy from collapse and Fed does so by primarily easing the supply of money into the economy. There are several ways it can ease monetary supply to the economy and some of the methods may include;
The Federal Reserve is responsible for choosing the specific interest rate best suitable for the U.S dollar at current market conditions. The emergence of strong indicators pointing towards an impending recession or deflation should therefore induce the Federal Reserve into lowering interest rates. By lowering interest rates, the Federal Reserve therefore will loan money to banks which will be repaid at a much lower interest rate (McCallum 19). Banks will then pass this on to consumers, who will be able to access funds more easily and pay back with low interest (Patinkin 82). This aims to stimulate spending, which in turn leads to profit making by companies and this brings about job creation thus maintaining the economy.
Another way of easing supply of money by the Federal Reserve is by expanding the threshold by which banks can access loans. This can be achieved through revision of the Fed lending policies and instead of lending to a bank based on the size of its reserve deposit, a loan can be granted based on the net worth of the bank. This way, more banks can have access to higher amounts of funds which will translate to more money in the economy.
Revising the percentage of standard reserve minimum deposits is another way the Federal Reserve can help increase the amount of money flowing through an economy. Banks are required to hold a certain percentage of their federal deposit and this amount is not suppose to be withdrawn unless if the bank wishes to close its reserve (Dewey 102). By reducing or removing the percentage of the deposit required to remain in the federal deposit, banks can have access to more funds and therefore have greater financial capacity to facilitate loans.
By introducing a flat tax rate, unemployment levels would drastically reduce for businesses and individuals would have more funds to spend. This can then stimulate growth of a deflated economy and increase the supply of money flowing through the economy.
To increase the amount of dollars being held in the reserves, the Federal Reserve can opt to unload some of the international currency and commodities held in the reserves by selling them to willing buyers. This in turn will increase the amount of dollars available for circulation into the market. In most cases, the sale of foreign currency and commodity reserves will yield a certain amount of profit which can be used to expand the financial base of the Federal Reserve.
The Federal Reserve can also attract international investors by facilitating credible investors with loans and investment options (Meltzer 39). The investors can also receive discount rates and prime rates from the Fed and other lending institutions. The investors will seek labour locally which means creating employment which leads to consumer spending and consequently availing fund to the economy.
Fixed interest rate and interest rate swap
Fixed rate position
A fixed rate position is holding on to a loan which has constant interest rate that does not change through out the repayment period. The interest rate is agreed upon between the lender and borrower prior to signing of any supporting documents.
Interest rate swap
This is a contractual agreement between two or more counterparties where one stream of future interest payments is exchanged for another different stream of interest payments based on a specific notional principal amount.
The fixed-for-floating interest rate swap is the most widely used form of interest rate swap and it entitles a series of payments calculated by applying a fixed rate of interest to a notional principal amount which is exchanged for a stream of payments similarly calculated but using a floating rate of interest (Meltzer 46). The money market swap or a basis market swap makes it possible for both streams of payment to be calculated using floating rates of interest but these floating rates are to be based upon different underlying indices. The indices include among others Libor, commercial paper and Treasury bill indices.
Since the value of the floating rate is adjustable, it is not easy to determine the future value of the floating rate (Friedman 57). However, available market data on forward interest rates can help in plotting a forward yield curve. It is through this graphical representation that one can be able to accurately estimate the value of the floating rate in order to make an informed decision. A receding floating rate creates losses for an investor while a rising floating rate will create profits. The forward yield curve would therefore rise if for instance soon after an interest swap, forward interest rates increase thus increasing the floating interest rates. The party making floating interest rate payments will therefore have to make higher payments in future than could have been expected in previous conditions, whereas the party making fixed interest rates payments will basically not be affected in their output since the fixed interest rate will remain unchanged. This benefit will be passed to the fixed rate payer under the swap and will represent a cost to the floating rate payer (Schwartz 65). Generally, the fixed rate payer is usually of lower credit standings than the floating rate payer. Interest rate swaps are more functional and applicable in markets where the counterparties belong to different markets, each with its own comparative advantage. This way, the counterparties can benefit from each others market resources. Interests swaps can also be terminated with agreement from all parties involve.
Termination of an interest rate swap transaction is concluded if there is an agreement between both parties, the accrued income either being divided in a given ratio or being awarded to the silent party. If for example a fixed rate payer wishes to end the swap, the acquired income should be passed on to the floating interest payer. A floating interest party who experiences a loss and is wishing to invest in a reverse swap with a new counterparty, then they will have to pay the new counterparty the current present value of the swap so as to maintain the original swap value. This ensures that the new counterparty does not experience sudden loss and that the value of a swap in controlled.
Interest rate swaps are utilised by a wide range of financial institutions like commercial banks, investment banks, institutions, companies including among others insurance companies, mortgage companies, investment vehicles and trusts, government agencies and self governing states among other parties (Friedman 66). Interest rate swaps serve as an attractive investment, this is because; they provide funding at a lower cost, they create a profitable investment opportunity which provide high yield in returns, they are used to hedge against interest rate exposure, speculators take up positions hoping for maximum returns and they are used to carry out strategies involved in management of assets and liabilities. This gives interest rate swaps a distinct number of advantages such as;
- Interest rate swap allows investing issuers to revise their transaction profile so as to take advantage of prevailing or impending expected future market conditions.
- A floating-to-fixed swap is a guaranteed way for an investor to make profit since both counterparties benefit in the long term.
- Fixed-to-floating rate swap could be of advantage to the floating interest rate payer in case of a decline in the floating interest rate since it means they will pay less to the fixed interest payer.
- Interest rate swaps when wisely invested in are potent financial tools that could lower the debt the issuer owes and at the same time provide an opportunity for profit generation.
As an investor currently holding a fixed rate position, I can mitigate some of the risks in my investments by using interest rate swap. I would enter into a fixed to floating interest rate swap and calculate the best point of entry using the forward yield curve. By this, I would pay my fixed rate in order for me to receive a floating rate indexed to a given percentage of the notional amount for a given period of time. By so doing, I will be converting my fixed interest rate liability into a floating rate asset. In order to make profit, the floating interest rate should however be increasing in value. A decreasing floating rate means a decrease in LIBOR and consequently this will translate into net loss.
|Scenario 2, if interest rate down||year 1||year2||year 3||year 4||year5|
|Fixed Rate Paid||9%||9%||9%||9%||9%|
|Floating rate received||7.50%||7.00%||6.00%||5.50%||5.00%|
|Net Dollar Amount Reveived|
|based on notional value of $100 Million||($1,500,000)||($2,000,000)||($3,000,000)||($3,500,000)||($4,000,000)|
A decreasing floating rate will therefore mean that the swap differential will be decreasing and hence the transaction will be in a loss. A good and profitable interest rate swap is one with increasing floating rate and hence an increasing LIBOR and swap differential.
|INTEREST RATE SWAP (Plain Vanilla Swaps)|
|Scenario 1, if interest rate up||year 1||year2||year 3||year 4||year5|
|Fixed Rate Paid||9%||9%||9%||9%||9%|
|Floating rate received||8%||8.50%||9.50%||10.50%||11.00%|
|Net Dollar Amount Reveived|
|based on notional value of $100 Million||($1,000,000)||($500,000)||$500,000||$1,500,000||$2,000,000|
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