What is Interest?
This article explains everything you need to know about interest and the jargon surrounding interest rates, that you will encounter when investing or borrowing money from banks.
If you would like to see how different interest rates will effect your loan payments and total interest paid, you can use this loan payment calculator.
The definitions I’ll cover in this post are:
- interest
- interest rate
- compound interest
- periodic interest rate
- nominal interest rate
- effective interest rate
Interest
- Interest is a fee, for the privilege of using borrowed money.
- Interest
If you borrow money, it comes at a cost. That cost is interest.
Similarly, you can make investments that pay interest. Your reward for making the investment is the interest you’ll earn.
The interest is usually expressed as an interest rate.
Interest Rate
- An interest rate is a percentage of the borrowed money, that the borrower has to pay as interest to the lender, over a period of time (usually a year).
- Interest rate
If the interest is not paid back to the lender at the end of the term, but instead added to the borrowed amount, the interest is compounded.
This means the interest payable at the end of the next term includes interest on the original amount borrowed, as well as interest on the previously accrued interest.
Compound Interest
- Compound interest is the interest payable on the original capital amount and any previously accrued interest.
- Compound interest
For example, if you borrow R1000 from someone, at an interest rate of 10% per year, and interest is compounded on a yearly basis, then you will owe:
- R1100 = R1000 + (R1000 x 10%) after one year,
- R1210 = R1100 + (R1100 x 10%) after two years,
- R1331 = R1210 + (R1210 x 10%) after three years,
- R1464 = R1331 + (R1331 x 10%) after four years,
- R1610 = R1464 + (R1464 x 10%) after five years, and so on.
Compound interest can cause the amount of interest to escalate very rapidly. Einstein called the effect of compound interest the eighth wonder of the world.
Nominal vs Effective Interest Rates
An important point to look at when making an investment or a loan, is the term over which interest is compounded.
Banks often express interest rates as a nominal figure, but they compound interest on a daily basis.
- The periodic interest rate is the percentage of interest charged at each compounding period. The periodic interest rate can be calculated by dividing the nominal interest rate by the number of compounding periods per year.
- Periodic interest rate
- The nominal interest rate is the periodic interest rate, multiplied by the number of periods per year.
- Nominal interest rate
- The effective interest rate is the total percentage of interest that accumulates on a loan, if interest is allowed to compound and no down-payments are made, for a year.
- Effective interest rate
For almost all loans the effective interest rate will be more than the nominal interest rate.
For example: a loan with a nominal interest rate of 9%, where interest is compounded on a daily basis, has an effective interest rate of:
(100% + periodic_interest_rate)^compounds_per_year – 100%
= (100% + 9%/365)^365 – 100%
= 9.42%
This is because a little bit of interest is added to the borrowed amount, every day.
The difference between nominal and effective interest rates can be significant. So make sure you read the fine print before you take out a loan, or make an investment.
This definition is part of the Dictionary of Financial Terms. If you want to receive a notice every time a new definition is published, you can subscribe to Liberta.
June 4th, 2009 at 10:54 am
Great article – certainly cleared some things up that I have been struggling with! Just two bugbears I noticed though – both in the definition of Compound Interest – firstly, a common mistake: you never lend anything FROM anyone, you borrow it (“For example, if you lend (should be BORROW) R1000 from someone, at an interest rate of 10% per year…”)
Secondly (not so essential, but still a bugbear of mine) – “Einstein called it the EIGHTH (not eight) wonder…”
Sorry for being anal, but I didn’t want your fascinating explanation to go tarnished by some basic language errors.
Thanks!
June 4th, 2009 at 10:21 am
@Duncan
Thanks for pointing out the mistakes.
October 7th, 2009 at 03:09 pm
Presume all calculations done before VAT, as VAT is state money? We are having a bit of a debate in the office.
Thanks
Esme
October 8th, 2009 at 11:03 am
@Esme
You’ve lost me here. Which calculations are you talking about?