Inflation and compounding are two basic concepts of economics and finance that you should understand. Together, inflation and compounding will have huge effects on your wealth over your lifetime. Related to inflation and compounding, present value and future value calculations are two basic personal finance formulas you should know. If you understand the concepts and know the formulas, you will be able to solve many time-related money problems.
If you are offered $100 either today or in 10 years, which offer should you accept? Most people will instinctively choose to take it today. But why? How does the value of the offers differ? How do we calculate the value of money over time?
Inflation
Inflation is the rise in general price levels over time, usually measured as the percentage change of the Consumer Price Index (CPI). Inflation will cause the purchasing power of our money to decrease.
What causes inflation?
1. Demand-pull inflation: Prices are often set by supply and demand. For example, you have tickets to a popular sold-out concert but cannot go because of personal matters, so you put it up for auction - the popular demand for the ticket will cause it to be sold at a premium over your purchasing cost. Similarly, when we (individuals, businesses, and governments) buy goods and services, if our demand exceed current supply, prices will rise.
2. Cost-push inflation: When prices rise for producers, they will pass the cost on to their customers so they can maintain their margins and profitability. It may be explicit cost transfers (such as the airfare fuel surcharges) or hidden cost transfers (price increase of McDonald's burgers).
3. Built-in inflation: As we see our groceries costs increase, we will ask for wage increases to cover our increased living expenses, and ask for more, so future price increases will be "covered" by this wage increase. We have priced both current inflation and future inflation into our wage increase. The companies we work for will then increase prices of the products and services so that margins are maintained. The price increase will ripple through the economy and eventually cause the price of our groceries to increase yet again. This is the vicious cycle of price/wage spiral.
Back to the $100 offer. How much purchasing power will the $100 have left in 10 years?
Time value of money: Discounting to present value
To calculate the purchasing power of $100 in 10 years, we will have to put the $100 in the future then "discount" it back to the present at the expected inflation rate (let's assume it as 3% p.a.) to find the purchasing power in present dollar value. The formula is as follows:
Where:
- PV is the value at time=0, the Present Value.
- FV is the value at time=n, the Future Value.
- i is the rate at which the amount will be discounted each period, the discount rate.
- n is the number of time periods.
For our example, the values we need to use are: FV = $100, i = 3% p.a., n = 10 years. When we solve the equation, PV = $74.41. This means that, in 10 years, your $100 will have a purchasing power equal to $74.41 today.
Compounding
Compounding is the addition of interest back to the principal, so that interest is earned on interest from that moment on. Instead of the linear growth of principal with simple interest, compounding will cause our principal to grow exponentially.
So what will happen to your $100 if you take it today and invest it for 10 years?
Time value of money: Compounding to future value
To calculate the amount of money $100 will become in 10 years, we will have to compound it at the expected compound growth rate (let's assume it as 6% p.a.) to find out how much money it will become in the future. The formula is as follows:
Where:
- PV is the value at time=0, the Present Value.
- FV is the value at time=n, the Future Value.
- i is the rate at which the amount will be compounded each period, the compound growth rate.
- n is the number of time periods.
Inflation, compounding, and the time value of the $100 offer
Inflation will decrease the value of $100 over time, whereas compounding will increase the value of $100 over time. Now that you have calculated the present value and future value of the $100 offers, rather than relying on gut feelings or instincts, you can compare them and make a rational decision on your offer.
| Take $100 today | Take $100 in 10 years | Difference | |
| Present value | $100.00 | $74.41 | $25.59 |
| Future value | $179.08 | $100.00 | $79.08 |
The effects of inflation and compounding make take the $100 today the better offer, no matter whether you look the present values or the future values of the offers. You will be better off taking the $100 today.
Related post:
Reference:
- Wikipedia
- Discount.
- Present value.
- Future value.
- Discount rate.
- Compound interest.
P.S. This post was featured in Carnival of Personal Finance #150 at Lazy Man and Money.
4 comments:
Good article on some basic financial principles. Though, I think you left out the first major cause of inflation in our modern society: the federal reserve. Our money is no longer based on anything with an inherent value (eg. silver, gold). Instead it is valued against the faith in the governments ability to pay you for your federal reserve note. When this faith decreases, so does the value of your dollar. The government did this in order to be able to fight wars whenever it wanted instead of having to go to the public for the funds. Now, instead of convincing people to sacrifice for a war effort, they just print more money out of thin air, which devalues your money. It's really just a brilliant way to tax you while blaming the devaluation on the "mysterious market force" inflation.
The problem you described is one inherent in fiat currency, where supply and demand will affect the currency's value. But be it fiat currencies or commodities (such as gold), they are only worth as much as people are willing to trade. Gold is only good as a currency because there is limited supply and limited manipulations.
Further on the concept of money and value, do commodities like gold or silver have "inherent value"? Circuit board makers find gold inherently valuable for use in "gold fingers". But I would argue commodities do not have inherent value for the general population - gold cannot be used to cook food or clean the house. A bartering arrangement where I cook two meals for you and you clean the house once for me, on the other hand, does have real value.
As you might see, I decided against discussing fiat currency, commodities, and the concept of money in my post because it is a complex and philosophical argument. If you are interested, Rob Ferguson published a couple of interesting posts at Free Money Finance on "money, currency, and wealth" and "purchasing power and inflation.
Excellent article. Thank you for writing this.
Possible typo: You have "(let's assume it as 6% p.a.)" and "For our example, the values we need to use are: PV = $100, i = 5% p.a., ..."
Did you mean 5% or 6%? Also, if the compound interest rate is the same as the inflation rate, it wouldn't matter if you took the money and compounded it or took the $100 ten years from now, right?
Well spotted - that was indeed a mistake and I've made the correction to 6%. Thanks!
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