Compound interest is the eighth wonder of the world. He who understands it, earns it…he who doesn’t…pays it.
– Albert Einstein
Understanding both the power of compound interest and the difficulty of getting it is the heart and soul of understanding a lot of things.
– Charlie Munger
The mechanics of compound interest are deceptively simple. You borrow a certain amount of money. You are liable to pay back the borrowed funds (called “principal”), plus an additional something (called “interest”) as cost of borrowing. Compound interest is the way this additional something is calculated.
Say the interest is charged annually.
By end of year one, you will be liable to an interest payment on the initial principal.
However, by end of year two, you will be liable to an interest payment on the initial principal plus interest from year one.
By year three, your liability becomes interest payment on the initial principal plus two years of interest!
This “interest on interest” is how compound interest works. And it can really add up.
An American children’s book author, Demi (née Charlotte Dumaresq Hunt) in a quaintly named mathematical folktale named “One Grain of Rice” describes the story of an Indian King, who is unwilling to open the royal granaries during a terrible famine, fearing he will run out of rice for himself. A village girl, through an accidental good deed ends up in the King’s court with his majesty granting her a reward of whatever she wishes. The girl deftly says that all she wants is one grain of rice. The king is surprised and pushes her to ask for more. The girl, having roped him in, complies and requests that her one grain of rice be doubled each day for the next thirty. So, starting with one grain on day 1, she can get two grains on day 2, four grains on day 3, and so on…
The King, amused at her “modest” expectations, grants her the wish. He doesn’t realize that thirty days later his granaries would be empty, thanks to the power of doubling. He didn’t understand the power of compound interest.
How is Compound Interest Measured? By something called the “interest rate”.
What are Interest Rates?
The percentage at which money compounds, be it in the savings account of your bank, or what you are liable to pay when you draw a loan, is called the interest rate. Interest rate is a broad, all-encompassing term. It can mean different things for different situations i.e. which country, which person, which business, and what time-frame. At its core, it is supposed to represent risk i.e. the risk of a borrower’s ability to pay back. An unreliable borrower would be charged a higher interest rate vs. a reliable one. The idea is that higher is the risk, higher should be the return. Similarly, if lower is the risk, lower should be the return.
This is not only true for people. The bank will ask for a higher interest rate from a small company vs. a large company. The bank realizes that the risk of financial instability is higher for the small company, hence they should be compensated for exposing themselves to this contingency. Even governments face this demarcation. The US government can borrow at a lower interest rate vs. the government of India. The United States is a much larger and more diversified economy. It is less likely to face financial distress vis-à-vis India, an emerging market where the government is more exposed to financial risks*. Extending the same logic, the government of India can borrow at a lower interest rate vs. the government of Assam. Lastly, the amount of time for which you have borrowed also determines the interest rate. If you’ve borrowed for a longer duration (say a 20-year home loan), you can expect to be charged a higher interest rate. Again, the risk of you not paying increases if the duration for repayment is longer. Note this relation is however not linear (more to be elaborated later).
How Do Interest Rates Work?
The country’s Central Bank drives short-term interest rates. However, it is the government which in a way sets their overarching tone over the long-term. The government earns revenue through citizens’ taxes, which they spend on public services and investments. For most, the revenues accumulated through taxes are less than the expenses. This deficit (technically called fiscal deficit) means the government often need to borrow money. It pays back interest when it borrows. This is the benchmark rate for the country, also euphemistically called the risk-free rate (strangely in the world of Finance, governments are risk-free).
Who Sets This Rate?
The creditors i.e. the ones who lends funds to the government by purchasing financial instruments called government bonds.
These creditors can be banks, pension funds, foreign institutions, and people. This supply demand dynamic between the borrower (i.e. the government) and the creditors sets the price – encapsulated by the risk-free rate.
All other interest rates in the country i.e. from when you take a bank loan or when you deposit monies in a savings account (simplistically) base themselves on this risk-free rate PLUS an additional percentage figure (also called the risk premium):
Interest rate for a particular transaction = Risk-free rate + Risk premium for the transaction
After all, unless you’re the government, you’re considered a riskier borrower. Hence you need to shell out more. If you’re a large established company, the risk premium will only be a couple of percentage points as you may be comparatively reliable. If you’re an individual, the risk premium will be set much higher. If you’re ready to pledge an asset, like a house or piece of land, as security for repayment of the loan (also known as “collateral”), your risk premium would reduce.
If you’re the government itself, the risk premium would theoretically be zero (conditions apply*).
The interest rate reflects the risk taken by your lender. Period.
*The government’s risk-free rate would also include a risk premium for the country in question (i.e. the “country risk premium”). That is why risk-free rate for the United States is lower than the risk-free rate for India. Read this detailed paper by Aswath Damodaran, Professor of Finance at Stern School of Business, New York University to know more on country risk premiums.
Published in partnership with Transfin.