Money and financial fundamentals

Start here to understand how money grows, what it can buy, and what you give up when you choose one use for it over another.

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No prior finance knowledge is needed. Each new finance term is bold, explained on first use, and linked to its glossary definition. The glossary links back to the section where you can see it in context.

The dollar amounts and rates below are invented teaching examples. Unless stated otherwise, assume no fees, taxes, additional deposits, or withdrawals, and a fixed annual interest rate with interest added once a year.

What money does

Money is something people widely accept to pay for goods and services and settle amounts owed. It includes physical notes and coins, as well as money held in bank accounts. A currency is a particular system of money, such as the US dollar, euro, or Japanese yen.

Money serves three jobs:

New term	Meaning	Everyday example
Medium of exchange	Something people accept in payment.	You pay for bread instead of finding a baker who wants something you own.
Unit of account	A shared unit for stating and comparing prices.	A $4 loaf costs twice as much as a $2 loaf.
Store of value	Something that can carry value into the future.	You keep money today to spend next week. What it buys can change.

These jobs explain why money is useful even when it exists as a number in an account. See the Bank of England’s explanation of money.

How interest works

Imagine putting $100 into an account that pays you for keeping money there.

The principal is the starting amount saved, invested, or borrowed: $100 in this example. Interest is money paid for the use of money. You may receive it on savings or pay it when you borrow.

An interest rate expresses that interest as a percentage of an amount over a stated period. “5% per year” means five dollars for each $100 over one year in this example. A percentage means “out of 100,” so 5% is 5 ÷ 100, or 0.05.

First year: $100 × 0.05 = $5 interest. You finish with $105.

Always look for the period attached to a rate: 5% per month and 5% per year describe very different costs. The Bank of England explains interest and interest rates.

With simple interest, interest is calculated only on the original principal. At 5% simple interest on $100, you earn $5 each year. After two years, you have $110.

How interest grows

Compound interest is interest calculated on both the principal and interest already added. Compounding is the process of adding earnings to the amount that can earn more. See Investor.gov’s compound interest definition.

Start again with $100 earning 5% per year, and leave all interest in the account:

Year	Amount at start	Interest for that year	Amount at end
1	$100.00	$5.00	$105.00
2	$105.00	$5.25	$110.25
3	$110.25	$5.51	$115.76

Amounts are rounded to the nearest cent. In year two, the extra 25 cents comes from earning 5% on the previous year’s $5 interest. Over longer periods, repeated growth can make a much larger difference.

The same process can increase what you owe if unpaid interest is added to a loan and itself starts attracting interest. The loan’s rules determine whether and when that happens.

Pause and check: Why is the second year’s interest $5.25 instead of $5? Because the amount earning interest has grown to $105.

What money can buy

Inflation is an increase in the general level of prices over time. One shop raising one price does not, by itself, tell you the overall inflation rate.

Purchasing power is the quantity of goods and services money can buy. When prices rise, an unchanged amount of money buys less. See the Bank of England’s inflation explainer.

Suppose your usual basket of groceries costs $100 today and the same basket costs $103 a year later. You need 3% more money to buy it. Keeping $100 without earning anything preserves the number of dollars, but it no longer pays for the whole basket.

This basket is a simplified example. Published inflation measures track many prices, and your own spending mix can change faster or slower than the reported average.

Measuring a gain or loss

A return is the gain or loss from saving or investing over a period, including money received and changes in value. It can be stated as money or as a percentage of the starting amount. See Investor.gov’s introduction to investing.

If $100 becomes $105 after one year, with no money added or removed, the gain is $5 and the percentage return is $5 ÷ $100 = 5%.

A nominal return measures that change before adjusting for inflation. A real return adjusts for inflation to show the change in purchasing power.

With a 5% nominal return and 3% inflation over the same year:

A quick estimate of the real return is 5% − 3% = 2%.
The exact calculation is (1.05 ÷ 1.03) − 1 = about 1.94%.

Why divide? Your money grew to $105, but a basket that used to cost $100 now costs $103. You can buy $105 ÷ $103 = about 1.0194 baskets: roughly 1.94% more than before. Subtraction is a useful approximation at low rates; it is not the exact calculation. The St. Louis Fed explains nominal and inflation-adjusted values.

A positive nominal return can still mean a negative real return when prices rise faster than your money grows. Fees and taxes, when applicable, also reduce what you keep.

Comparing money at different times

The time value of money is the idea that when you receive or pay money affects its value. Money available today can be used now or earn interest before a future date.

Suppose you can earn a certain 5% over one year. Under that assumption, $100 today can become $105 next year. Those amounts are equivalent for that comparison. This timing effect exists even without inflation.

Future value is what an amount today would grow to by a future date at an assumed rate. Here, $100 × 1.05 = $105 after one year.

Present value is today’s equivalent of a future amount using a chosen rate. Working backward, $105 ÷ 1.05 = $100 today.

Discounting is that backward calculation. The discount rate is the rate used in it: 5% here. It is an assumption for comparing amounts at different times, not a discount offered by a shop. These concepts are covered in the St. Louis Fed’s time value of money course.

For two years at the same annual rate:

Forward: $100 × 1.05 × 1.05 = $110.25.
Backward: $110.25 ÷ 1.05 ÷ 1.05 = $100.

Multiplying or dividing once for each year keeps the calculation easy to follow. A higher positive discount rate produces a lower present value for the same future payment. The appropriate rate depends on the available alternatives and how uncertain the payment is; 5% is only our example assumption.

Weighing risk and access

Risk is uncertainty about a financial outcome, including the possibility of losing money or falling short of what you need. A hoped-for return is not a promised result. Taking more risk does not guarantee that you will earn more. See Investor.gov’s guide to investment risk.

Liquidity describes how easily and quickly something can be turned into spendable money without a large loss in value. See Investor.gov’s liquidity definition.

For example, money in an account that allows immediate withdrawals is usually easier to use for tomorrow’s bill than a bicycle you need to sell. You might need time to find a buyer, or accept a lower price to sell quickly.

Liquidity and price stability are different questions. Something can be easy to sell while its price changes sharply. Money you can access immediately can still lose purchasing power through inflation.

When comparing choices, ask: What could go wrong? When will I need this money? Can I get it back in time, and at what cost?

What you give up

Opportunity cost is the value of the best alternative you give up when making a choice. It can involve money, time, convenience, or something else you value. The St. Louis Fed explores opportunity cost in everyday decisions.

Suppose you have $100. You could buy a concert ticket now or save the money at our assumed 5% annual rate. If saving is your best alternative, choosing the concert means giving up having $105 next year. The $5 is the interest you forgo; the full alternative is the $105 future balance.

Choosing to save also gives something up: the experience of attending the concert. The calculation makes the tradeoff visible; your needs and preferences determine how much each option matters.

Check your understanding

Try these before reading the answers:

You save $200 at 5% annual compound interest. How much do you have after two years?
Your money earns 2% in a year while prices rise 4%. Has your purchasing power increased?
At a 5% annual discount rate, what is the present value of $210 received one year from now?
An item is worth $500, but selling it may take weeks. Which term describes the difficulty of turning it into money quickly?
You spend an evening studying instead of working a paid shift, your best alternative. What have you given up?

Answers

$220.50. First year: $200 × 1.05 = $210. Second year: $210 × 1.05 = $220.50.
No. The real return is (1.02 ÷ 1.04) − 1, or about −1.92%. You have more dollars but can buy less.
$200. Divide $210 by 1.05 to work backward one year.
Liquidity. The item is less liquid because finding a buyer takes time; a quick sale might require a lower price.
The value of the paid shift, including its earnings. That is the opportunity cost of choosing to study in this example.

Terms introduced in this lesson

Use these links to revisit definitions. Each glossary entry has a link back to its explanation above.

Keep learning

Continue with Personal finance and financial wellbeing to apply these ideas to a household budget, savings, and borrowing. Continue with Banking, credit, and lending to compare deposit accounts and work through loan repayments.