Question

Which statement is true? (LO5) a) A dollar today is worth more than a future dollar because of inflation. b) A dollar in the future is generally worth more than a dollar today. c) There is no way to determine whether a future dollar is worth more or less than a dollar today. d) A dollar today is worth more than a dollar in the future.

Short answer

The true statements are: a) A dollar today is worth more than a future dollar because of inflation. d) A dollar today is worth more than a dollar in the future.

Step-by-step solution

Understand the time value of money

In order to answer this question, we need to understand the concept of the time value of money. The time value of money is the notion that a certain amount of money is worth more today than it will be in the future because it has the potential to earn interest or generate returns if invested today. Inflation also plays a role in this concept, as inflation generally increases over time, decreasing the purchasing power of money in the future.

Evaluate each statement

Let's examine each statement to determine which is true. a) A dollar today is worth more than a future dollar because of inflation. This statement is true. Inflation is the general increase in prices over time, causing the purchasing power of money to decrease. Therefore, a dollar today will generally be able to purchase more than a dollar in the future. b) A dollar in the future is generally worth more than a dollar today. This statement is false. As explained earlier, the time value of money and inflation cause a dollar today to be more valuable than a dollar in the future. c) There is no way to determine whether a future dollar is worth more or less than a dollar today. This statement is false. While future inflation and other factors may be uncertain, it is generally assumed that the time value of money and inflation will cause a dollar today to be worth more than a future dollar. d) A dollar today is worth more than a dollar in the future. This statement is true, as it essentially restates statement a, although in a simplified manner.

Select the correct statement

The true statement is both a) A dollar today is worth more than a future dollar because of inflation and d) A dollar today is worth more than a dollar in the future.

Key concepts

Inflation

In simple terms, inflation is the rate at which the general level of prices for goods and services is rising, and subsequently, purchasing power is falling. Central banks attempt to limit inflation, and avoid deflation, in order to keep the economy running smoothly. Imagine going to the store with one dollar and being able to buy a loaf of bread today, but a year from now, that same dollar might only get you half a loaf. That's inflation at work.

In context to the time value of money, inflation is a crucial factor because it erodes the real value of money over time. As prices increase, each unit of currency buys fewer goods and services. This is why investors seek opportunities where the return exceeds the rate of inflation, to ensure that their money's worth is not diminished in the future. Understanding how inflation impacts the value of money can help students effectively plan their investments and savings strategies.

Purchasing Power

Purchasing power refers to the value of currency expressed in terms of the amount of goods or services that one unit of money can buy. It's directly impacted by inflation and deflation. In an inflationary environment, the purchasing power of money decreases because you can buy less with the same amount of money. On the other hand, if deflation occurs, purchasing power increases, as prices of goods and services drop.

For example, if last year one could buy a cinema ticket for \(10 and this year the price is \)12, assuming your income hasn't changed, your purchasing power has decreased. It is vital for students to grasp this concept because it has real-world implications on their budgets, savings, and lifestyle. It is an important consideration for anyone making long-term financial plans.

Interest Rates

Interest rates are essentially the cost of borrowing money. They are central to the time value of money equation as they represent the potential return on investment. When money is deposited in a savings account, it earns interest, meaning the money will grow over time. Conversely, when money is borrowed, interest must be paid to the lender, meaning the cost of borrowing will increase over time.

In terms of time value of money, if interest rates are higher than the inflation rate, the real return on savings or investments is positive, making a dollar today potentially worth more in the future if invested wisely. Students should understand that while saving money is important, where they keep their money—whether in a bank account, stocks, bonds, or other assets—could significantly impact its future value due to varying interest rates.