How Money Really Works, Part 4: How Interest Makes Money Grow

7. The price of money

How interest makes money grow, in seven parts, from the rate your bank pays to money that doubles. Number seven: you read every rate on a bank page as a price, because the IMF calls interest the cost of money. Once you know it, every rate on a bank page makes sense. Most people miss that interest pays for two things at once.

It pays for the use of the money and for the risk the lender takes. The IMF says it plainly: interest is the cost of credit or the cost of money. For most of history, the IMF says, the rates borrowers pay on loans have been above zero. A borrower signs to pay back the loan plus an amount that compensates the lender.

That amount pays the lender for using her money and for the associated risks. The IMF says theories point to the supply of savings and the demand for investment. When you save at a bank, you are the lender. Your savings book shows the interest the bank pays to you for the use of your money.

The World Bank notes that interest-rate terms differ from place to place, limiting their comparability. So a rate on one page cannot always be set beside a rate on another. Rates and rules also differ where you live, so your own bank page shows your own terms. A loan for ten years and a loan for one month carry different rates, and number six shows why.

Subscribe so the next parts of this series reach you: every figure here comes from the IMF or the World Bank, linked below.

6. Why time raises the rate

For number six, you set a one-month deposit beside a ten-year one, and see why time raises the rate. The rate is also a price for waiting, and a longer wait usually earns a higher rate. The IMF says interest rates must be positive to motivate saving. The IMF adds that investors demand progressively higher interest rates the longer money is borrowed.

That higher rate compensates for the heightened risk involved in tying up their money longer. A lender who locks money away for years sees a longer date on the contract. The IMF puts it this way: under normal circumstances, the longer the term, the higher the interest rate would have to be. Inflation joins the picture, because it is the rate at which money loses value.

The IMF splits what a lender gives up into two parts: keeping pace with inflation, and a real return on top. The IMF says that to know what an investment yields or what a loan costs, we account for inflation. It also says expectations of inflation are a key driver of longer-term interest rates. The same idea shows up in bonds, where the IMF says longer-term bonds usually carry a higher yield.

The IMF calls that extra yield the term premium. For your own money, lending for a longer time usually earns a higher rate, as the IMF describes it. That pattern holds only under normal circumstances, and rates and rules differ where you live. Next, number five: what your own bank actually pays you for the money in your account.

5. What your bank pays you

Number five: you open your savings book and find the rate your bank pays you. The World Bank defines the deposit interest rate as the rate paid by banks for demand, time, or savings deposits. Your savings book shows that rate, the price the bank pays for holding your money. The World Bank defines the lending rate as the bank rate meeting short- and medium-term financing needs of the private sector.

A borrower signs to pay back the loan plus interest at that higher rate. By our count of World Bank data, the median deposit rate in twenty twenty-four was about 3.7%. By our count of World Bank data, the median lending interest rate in twenty twenty-four was about 9.8%. By our count of World Bank data, the median interest-rate spread in twenty twenty-four was about 5.5 percentage points.

The IMF says banks perform a key function by matching savings to useful projects that generate a high rate of return. In turn, the IMF says banks earn a spread, the difference between what they pay depositors and what they charge on loans. Your account balance grows by the deposit rate, while the bank keeps the spread for matching savers and borrowers. The World Bank notes that these terms differ from place to place, limiting their comparability.

The medians cover only the economies that report each rate, so they describe a middle, not every account. The rates on your own savings book and loan papers differ from these medians where you live. In one breath: interest is the price of money, time raises it, and your bank pays you less than it charges. Next come the rates that move all the others, and what is left of interest after prices rise.

At number four, you follow one rate, a central bank's

4. The rate that sets the others

policy rate, which sets the tone for the others. Knowing it helps you read why the rates on your own bank pages move. One rate set by a central bank influences many other rates, mainly short-term ones. The IMF says the policy interest rate provides the key benchmark for borrowing costs in an economy.

In modern times, central banks charge a positive rate when they lend short-term funds, the IMF notes. The IMF says central banks vary the policy rate as the economic cycle changes. They also use it to steer an economy by influencing many different, mainly short-term, interest rates. For your money, the IMF says higher policy rates provide incentives for saving.

Lower rates motivate consumption and reduce the cost of business investment, the IMF adds. The IMF also describes a neutral rate, the long-term rate consistent with stable inflation. The IMF says that neutral rate neither stimulates nor restrains economic growth. When rates sit below the neutral rate, the IMF calls policy expansionary, and above it, contractionary.

The policy rate steers mainly short-term rates, not every rate on a contract. Rates and rules differ where you live, so each bank's page shows its own numbers. Quick guess before number three: if a loan pays 2% while prices rise 3%, does the lender gain?

3. Interest after inflation

Here's number three: you subtract inflation from your rate to see what your interest really buys. Part three of this series showed why prices rise, and this is what it means for your interest. Most people miss that a lender can receive interest in cash and still end up with less buying power. The IMF's example has inflation at 3% and a loan rate of 2%.

The IMF says the lender's return after inflation is then less than zero, even though interest is paid. The real interest rate is the nominal rate minus the rate of inflation, says the IMF. By our count, 2% minus 3% is minus 1% after inflation. The World Bank measures it for loans: the lending interest rate adjusted for inflation, using the GDP deflator.

By our count of World Bank data, the median real lending rate in twenty twenty-four was about 5.3%. For your own money, the rate printed in your savings book is one number, shown on the page. The growth of what your savings can buy at the shop is a second number. That second number is the rate in your savings book minus the rate of inflation.

The World Bank's real rate is for bank loans, not for savings accounts. Loan terms differ from one economy to another, the World Bank notes. Rates and prices differ where you live, so each savings book sits beside its own prices. If you want the full picture on prices, the video on protecting your money from inflation is linked on screen.

In one breath: one central bank rate steers the others, and inflation decides what interest really buys. The last two show how the price you pay and the time you wait change what interest adds.

2. Bonds and their yield

With number two, you lend to a government by buying a bond, and its yield shows the return on what you pay. The IMF calls a bond a promise by the government to repay $100 of principal. The bond also pays annual interest to investors, which the IMF calls a coupon payment. The price an investor pays for a bond can sit below its face value.

In the IMF's example, the government issues a one-year bond with a coupon rate of 5%. Governments issue bonds that run from one year to thirty years, the IMF notes. That is a commitment to pay investors $105 after one year. Of that amount, $100 is principal and $5 is interest.

The $5 of interest is the coupon, 5% of the $100 principal. If that coupon matches what investors could earn elsewhere, they pay the full $100, the IMF explains. In the IMF's example, investors are willing to pay only $98 for that same bond. They still receive $105, so their return rises to 7.1%.

The IMF calls this total return the bond's yield, or yield to maturity. Each bond has its own coupon rate and its own yield to maturity, the IMF adds. Bonds can also change hands between investors, the IMF notes, because they are tradable, like stocks. The IMF also says longer-term bonds usually carry a higher yield, called term premium.

The IMF says higher expected inflation and higher returns elsewhere raise what a government must offer investors. For your own money, a bond's yield depends on the price paid, not just the printed coupon. These are the IMF's example numbers for a bond, not a rate on offer to anyone. Rates and rules on bonds differ where you live, so the example stays an illustration.

Before number one, take a guess: at a rate under 4%, how many years does money take to double?

1. Interest on interest

Number one: you leave the interest in, and interest on interest doubles money, even at a rate under 4%. The difference between leaving interest in and taking it out is small at first and grows with time. When the interest stays in your account, next year's interest is figured on a bigger balance. By our count, after the first year both ways add up to $1,036 and eighty cents.

Your balance on the statement then earns interest on the interest, not only on the first deposit. By our count of World Bank data, the median deposit rate in twenty twenty-four was about 3.7%. By our count, $1,000 at 3.68% grows to about $1,435 in ten years. That is with the interest left in the account.

Taking the interest out each year instead leaves $1,368 after ten years, by our count. The gap after ten years is $67, as the two balances on the page show. By our count, after twenty years the balance with interest left in is about $2,060. Taking the interest out each year leaves $1,736 after twenty years, by our count.

After twenty years the gap is $324, larger than at ten years. By our count, at that rate the money doubles in a little over nineteen years. The longer your money stays in the account, the more interest on interest it adds. What the balance buys still depends on the rate minus inflation, the real rate.

These counts assume the same rate every year, and a bank's posted rate changes over time. Rates and rules differ where you live, so your own savings book may show other numbers. That's all seven, so here is the whole picture of interest in seven short lines.

Recap

Number seven: interest is the price of money, paid for its use and for the risk. Number six: the longer money is lent, the higher the rate usually is. Number five: banks pay savers less than they charge borrowers, and earn the spread. Number four: a central bank's policy rate is the benchmark for the others.

Number three: the real rate is the rate minus inflation. Number two: a bond bought below its face value pays a higher yield. Number one: interest left in earns interest of its own, and time does the rest. Which of these seven surprised you most?

Tell us in the comments. Results vary, rules differ where you live, and this is information only, not financial advice. Next on Wealth Filings, part one shows why money is a promise, from coins to the balance in your bank, linked on screen.