Time Value of Money Explained (2026): PV vs FV Made Simple

Money doesn't maintain its value over time. One Canadian dollar today will be worth less than a single dollar in the future, as it can be invested, earn returns, and needs to keep up with inflation.

Understanding the concept of time value of money (TVM) is essential as it explains how savings grow, influences financial decisions, and determines how money is borrowed.

What is the time value of money and why does it matter?

Timing affects how much money is worth. The same amount today will hold more value than in the future:

What is the time value of money?

Time value of money (TVM) is a concept that explains why the value of money will be worth more today than the value of money in the future. Because money can be invested, earn interest, and generate capital gains, its value over time increases, while inflation diminishes its purchasing power. This idea matters, as it is often used to drive decision-making when investing, borrowing, and saving money.

It also applies to everyday scenarios, such as retirement savings, evaluating investment opportunities, and mortgage payments. In other words, it demonstrates why obtaining money sooner, rather than later, is often more valuable.

What is the core idea behind TVM?

The underlying principle of time value of money (TVM) is that money today can grow into more money tomorrow. For example, if someone invests $1,000 at a 5% annual interest rate for five years, the principal amount will grow to $1,276. This growth increases gradually as more time passes. Therefore, money received at an earlier date will have more time to grow, and it's this growth potential that makes receiving money sooner preferable.

The rate of return shown is used only to illustrate the effects of the compound growth rate and is not intended to reflect returns in any specific investment and is not to be considered as investment advice.

Why is money today usually more valuable?

There are three main reasons why money today holds more value than in the future:

• Opportunity cost: Money today can be invested and potentially earn positive returns.

• Inflation: Prices of goods and services generally rise over time, which can reduce how much money can purchase.

• Uncertainty: Future payments are never 100% guaranteed due to being delayed, smaller than anticipated, or never being received.

Because of these risk factors, money today is generally considered to be more valuable.

Why is money today worth more than money tomorrow?

Money someone receives today has benefits that future money does not, which stem from growth potential, inflation, and risk:

How does earning potential increase value?

Money that's available right now can be invested immediately, whether it is in a high-interest or tax-advantaged savings account, bonds, or a diversified investment portfolio. As time goes on, this money can grow as a result of compounding.

For example:

$100 invested per month for 30 years at a compounding interest rate of 7% would equal approximately $121,997.

• Total contributions: $36,000

• Growth: Approximately $85,997.

This illustrates how time and consistency can significantly increase the value of money.

The rate of return shown is used only to illustrate the effects of the compound growth rate and is not intended to reflect returns in any specific investment and is not to be considered as investment advice.

How does inflation affect future money?

Inflation is a factor that reduces the purchasing power of money over time. The Bank of Canada targets inflation at 2% (opens in a new tab), meaning the price of goods and services will gradually increase year after year. For example, $100 today won't buy as much 10 years from now. Savings must grow to maintain the value of money. Without growth, money will lose value.

Why do risk and delay matter?

Future money is less guaranteed than money today. A future payment could:

• Be delayed and will not arrive as planned.

• Be smaller than anticipated due to market volatility.

• Not come at all.

Ultimately, there is always some level of risk when it comes to future money and its value, which is why money today is more reliable and valuable.

What is the difference between present value and future value?

Present value and future value are two approaches used to measure how money changes over time. Together, they help compare amounts that occur at different points in time:

What is present value (PV)?

Present value calculates what the future amount of money is worth today. The following formula is used:

PV = FV / (1 + r)ⁿ

• PV (Present Value): Value of money today.

• FV (Future Value): Value of money in the future.

• r: Interest or discount rate.

• n: Number of compounding periods.

For example, if you anticipate receiving $1,000 in five years, the present value will be less than $1,000 today, because money can earn returns during those five years.

What is future value (FV)?

Future value calculates how much money today can grow over time. This can be calculated using the following formula:

FV = PV × (1 + r)ⁿ

• PV: Current amount of money invested.

• r: Interest rate.

• n: Number of compounding periods.

For example, $1,000 invested at 5% annually for five years will grow into a larger amount due to compounding interest. This growth happens because each year's investment returns are added to the total value.

How to calculate the time value of money?

Time value of money (TVM) calculations use a set of variables that will determine how money grows or decreases over time.

What variables are used in TVM calculations?

A time value of money formula uses the following variables:

• Present value (PV)

• Future value (FV)

• Interest rate or discount rate (r)

• Time period (n)

• Compounding frequency

Each variable plays a primary role in the total outcome. Even minor changes can have notable differences in outcomes over longer compounding periods.

What role does the discount rate play?

A discount rate converts future value into present value. It may represent:

• Expected investment returns.

• Costs associated with borrowing money.

• Returns adjusted for inflation.

A higher discount rate will reduce the present value of money because there's a possibility the money may grow faster somewhere else. For example, if you expect to receive $1,000 in five years, a discount rate of 5% would mean the present value of the money is around $783. With a discount rate of 10%, the present value will decrease to approximately $620.

How do compounding and discounting work?

Compounding and discounting methodologies help explain how money changes over time.

What is compounding?

Compounding is used to calculate growth when interest rates are added to the original invested amount and previously earned interest. For example, if an investor invests $1,000 with a compounding interest rate of 5% annually, the following growth would occur:

• Year 1: $1,050.

• Year 2: $1,102.50

• Year 3: $1,157.63.

Compound interest is a snowball effect that makes the total balance grow faster over time compared to simple interest, where interest is only calculated on the original $1,000 each year.

The rate of return shown is used only to illustrate the effects of the compound growth rate and is not intended to reflect returns in any specific investment and is not to be considered as investment advice.

What is discounting?

Discount rates work oppositely to compounding rates. It calculates what a future amount is worth today, while taking into account time, expected returns, and opportunity costs. Both methodologies use the same math but move in different directions.

Using the original example above:

• Future value: $1,157.63 (sum after 3 years of 5% compounding).

• Discount rate: 5% per year.

• Formula: PV = FV ÷ (1 + r)ⁿ

• Calculation: PV = $1,157.63/(1.05)^3= approximately $1,000.

What are real-world examples of the time value of money in Canada?

The time value of money (TVM) shows up in many everyday financial situations:

Long-term savings and investing

Retirement savings accounts use compound interest to grow funds. Starting earlier allows money to grow over a longer time horizon, which can lead to greater returns.

For example:

• $10,000 invested at a 7% compound interest rate for 30 years grows to approximately $76,123.

• $10,000 invested at a 5% compound interest rate for 30 years grows to around $43,219.

This illustrates how even a small difference in interest rates and starting times can create a larger effect in earnings. Ultimately, regular contributions can accelerate growth, making long-term planning essential for retirement and wealth accumulation.

The rate of return shown is used only to illustrate the effects of the compound growth rate and is not intended to reflect returns in any specific investment and is not to be considered as investment advice.

Mortgage and loan payment timing

When it comes to borrowing money, interest increases the total cost owed over time. Longer repayment periods may make monthly payments lower, but it often results in having to pay more interest over time.

For example:

A $200,000 mortgage at a 5% interest rate over 25 years will result in a higher total interest than over 15 years.

By understanding how the time value of money (TVM) functions, borrowers can uncover the actual cost of debt and plan more informed repayment strategies.

Inflation and purchasing power

Even if an investor's savings grow, inflation still reduces purchasing power. This means they can buy less with the same amount of money in the future, which is why long-term savings like retirement should aim to outpace inflation.

For example:

If inflation averages 2% a year, $100 today will need an additional $20 in about 9 years to purchase the same amount of goods and services. When planning financial goals, accounting for inflation ensures that savings and investments maintain real value over time.

Comparing cash-flow options

Time value of money (TVM) formulas also help evaluate financial decisions like income and payment periods. For example:

A $1,000 lump sum payment today may be more valuable than $350 per year for three years, as someone could take the $1,000, invest it, and grow that $1,000 to more than the total of future payments.

Using time value of money (TVM) can help compare different options and ensure decisions about saving, borrowing, and investing take into account both time and amounts to provide a better picture of the true value of money.

What rate should you use in time value calculations?

When using the time value of money formula, choosing the right rate is key, as it will directly affect the value of money over time. A higher rate assumes that the money could earn more if it were invested somewhere else, which will reduce the present value of future cash flows. In contrast, a lower rate will assume a slower growth rate or lower returns, meaning that future money will be considered as closer in value to its present value.

Expected investment returns

When calculating potential investment opportunities:

• Use realistic long-term returns.

• Diversified Canadian stock portfolios historically return around 5% to 8% annually.

• Using expected return rates aids in projecting how money today can grow over time.

Past performance is not an indicator of future results

Borrowing or opportunity cost rates

For loans and other financial decisions:

• The interest rate will become the discount rate.

• This shows the cost of delaying payments or taking on debt.

• Comparing borrowing costs to investment opportunities can help determine effective choices that align with financial goals.

Inflation-adjusted rates

• Actual returns account for inflation.

• Using rates adjusted with inflation in mind ensures calculations mirror the actual value.

Common mistakes that investors could make when using TVM

Even minor errors in calculating TVM can distort results:

Using the wrong time period

Using the wrong compounding period can generate inaccurate results. Ensure there is consistency in time variables and interest rates in the formula.

Using an incorrect interest or discount rate

Over-projecting expected returns will inflate future values of money, while under-projecting discount rates will exaggerate present value. Choose a rate that reflects the situation at hand.

Ignoring inflation effects

Nominal amounts only show the dollar value, not how much those dollars can actually buy. Always consider the real value of money when planning long-term financial goals.

Mixing nominal and real values

Using nominal rates with actual cash flows can lead to errors, and vice versa. Ensure the rate and money amounts are expressed in the same terms.

Conclusion: why the time value of money is a key financial concept

Money has different values depending on timing. Receiving money today is often preferred over receiving it later, because that money can grow and reduce uncertainty. By understanding how the time value of money works, Canadians can make smarter investment and savings decisions, compare loans, and plan long-term financial goals.