Time Value of Money

Price Inflation

Inflation Defined

The most indicative input to the time value of money is inflation, which impacts purchasing power and investing.
Inflation can have significant implications on purchasing power. Purchasing power is a measure of how much of a good or service can be bought with a certain amount of money. Compounding interest can affect how much money someone has over time; however, purchasing power is limited by the rate of inflation over the same period. Future value (FV) can be calculated.
FV=PV(1+r)n\text{FV}=\text{PV}\;(1+r)^n
Where:
FV=Future ValuePV=Present Valuer=Raten=Time Period\begin{aligned}\text{FV}&=\text{Future Value}\\\text{PV}&=\text{Present Value}\\r&=\text{Rate}\\n&=\text{Time Period}\end{aligned}
For example, after 10 years an investment of $1,000, or the present value (PV), growing at an interest rate of 10 percent compounding annually would equal $2,593.74.
FV=$1,000(1+0.10)10=$2,593.74\begin{aligned}\text{FV}&=\$1{,}000\;(1\;+\;0.10)^{10}\\\\&=\$2{,}593.74\end{aligned}
Over this same period, if inflation grew at a rate of 5 percent annually, then in terms of increased purchasing power, the net, or difference, in the compounding interest rate would be 10 percent minus 5 percent, or 5 percent. Using the future value formula, this would leave an inflation-adjusted value of $1,628.89 after 10 years in terms of a real increase in purchasing power above the original $1,000 investment of principal.
FV=PV(1+r)n=$1,000(1+0.05)10=$1,628.89\begin{aligned}\text{FV}&=\text{PV}\;(1+r)^n\\\\&=\$1{,}000\;(1+0.05)^{10}\\\\&=\$1{,}628.89\end{aligned}
However, if the inflation rate were only 3 percent instead of 5 percent, then the compounding interest spread would be 10%3%10\%-3\%, or 7 percent. Using the future value formula, the increase in purchasing power after 10 years can be calculated and would be $1,967.15. The key for an investor is that the actual benefit of investing in terms of increasing one's purchasing power over time is a combination of the investment return and the impact of inflation over an equal time period.
FV=PV(1+r)n=$1,000(1+0.07)10=$1,967.15\begin{aligned}\text{FV}&=\text{PV}\;(1+r)^n\\\\&=\$1{,}000\;(1+0.07)^{10}\\\\&=\$1{,}967.15\end{aligned}
The impact of inflation on the time value of money can influence both business and personal considerations when it comes to investing. Banks, for example, lend money at various interest rates to people to purchase homes and cars or to purchase items via credit cards and unsecured loans. Banks also borrow money from individuals by promising them guaranteed rates of return on certificates of deposit (CDs), which are tied to interest rates, for investments over set periods of time. In order to get people to purchase a CD for an investment, a bank must promise a rate of return that instills confidence that it will be higher than the rate of inflation over that same time period. Otherwise, a CD could cause investors to lose purchasing power in what should be a safe, guaranteed investment. Conversely, when a bank lends money to consumers so they can purchase homes and cars, the bank must charge a high enough interest rate to both surpass inflation and exceed what it is willing to pay out in CD rates. The spread between the rate a bank is willing to lend in comparison to what consumers are willing to pay to borrow is the bank's profit. In general, as interest rates gradually increase, due to inflation, the value of an investment decreases. As interest rates are lowered, consumers are able to borrow more money. The result is that consumers have more money to spend, causing the economy to grow and inflation to increase. The opposite holds true for rising interest rates.

Impact of Inflation over Time

This is an illustration of the impact of inflation on the real value of a dollar over time at various rates of inflation.

Inflation and Purchasing Power

Demand-pull inflation and cost-push inflation can cause elevated price levels in a product or service and increase the velocity of money.

Inflation is the rise of the general level of prices. A common measurement of inflation is the consumer price index. The consumer price index (CPI) is a monthly measure that reflects the price increase or decrease of a core number of consumer goods and provides an indication of inflation or disinflation over time. The CPI is released by the federal government. Tracking this number over time provides information about inflation in a broad national sense.

Inflation can be caused by a variety of factors, but the primary two are demand-pull inflation and cost-push inflation. In demand-pull inflation, an increase in consumer demand for a product or service causes an increase in price levels. People are willing to pay more for the same goods and services than they previously were because of the scarcity of the items. The products become more expensive as measured by the inflation rate. In cost-push inflation, increased production costs, such as for raw materials and labor, cause elevated price levels. This leads to a rise in the inflation rate.

These influences on inflation happen on a broad macroeconomic scale. However, there are individual differences in certain industries or areas that can have a significant impact on the overall economy and on investment and purchasing decisions. For example, in recent decades the cost of college tuition has risen at a rate that greatly exceeds the growth in CPI over the same time period. This means that for many college students the cost in real dollars of obtaining a degree is significantly higher than it was for their parents and grandparents. Other areas, such as health care costs, have also risen in price over the years, and much faster than other items. The opposite can also occur during recessionary economic times. The housing crisis in the United States that began near 2009 resulted in significant declines in the average price of many homes following years of significant appreciation in home values. Individuals who bought or sold a home during this turbulent period for the housing market often saw significant increases or declines in their overall wealth, depending on which side of the housing transaction they were on.

Causes and Reduction of Inflation

The historical timeline of finance is full of examples of economic cycles of high inflation and recession.

The greatest period of economic decline since the Great Depression stemmed from weaknesses in the housing market from excessive subprime mortgages going bad starting around 2009. During times of economic contraction, inflation is often flat or even slightly negative as demand for goods and services drops. Economic conditions tend to move in cycles, however. After periods of turbulence and economic downturn, the economy usually bounces back with lower rates of unemployment, easier lending standards, and increased demand for goods and services, which lead to inflation. In response to increased demands, when the economy is ramping up, the government often employs various tools to help keep inflation in check and prevent it from growing too fast.

The Federal Reserve is the central bank of the United States and is in charge of setting monetary policy in the United States. Monetary policy involves the actions of the central bank, current board, or other regulatory committee that determine the size and rate of growth of the supply of money, which in turn affects interest rates and inflation. The Federal Reserve is most directly responsible for implementing policies to help improve the economy during recessionary times and to lower inflation when the economy is strong and robust. There are several tools that the Federal Reserve utilizes to lower inflation when it feels that prices are rising too quickly. It can reduce the money supply in the economy by increasing interest rates. Banks borrow money from the central bank, which they then lend to others at a spread premium. Thus, when the Federal Reserve increases the rate at which it is willing to lend to banks, the banks necessarily raise the rates they charge consumers for loans. This can slow inflation because demand, in turn, decreases for most goods and services as it becomes more expensive for consumers to borrow and spend.

The Federal Reserve can also contract the money supply and reduce inflation by requiring banks to increase the amount of money they must keep on hand in reserves, reducing the amount they are allowed to lend. Finally, this governmental board can reduce the amount of money in the economy by increasing the interest rate it is willing to pay on federal bonds, encouraging investors to buy more government bonds as opposed to investing in the stock market and other economy-boosting investments.