How are term deposit and credit card interest calculated? Simple vs Compound Interest

Simple interest is the most basic type of interest.  Simple interest is just the interest rate percentage times the original capital (see diagram below).  Some term deposit accounts are calculated using simple interest. In term deposit accounts the interest is usually calculated at the end of each year.

62776339-A852-4CF8-8228-772D0B3F8494Under a simple interest loan, if I borrow $1 and the interest rate is 10% p.a. then I will need to repay $1.10 after 1 year.

Total repayment = Principle + Interest

=  $1 + ($1 x 10%)

= $1.10

 

Some term deposit interest rates are instead calculated using compound interest. This also goes for credit card interest, personal and home loan interest or even the interest you get on most regular savings bank accounts. The interest on these types of loans and savings is calculated using compound interest. That is interest that is compounded. With compound interest, you pay interest on not just the principle but on interest you haven’t paid off yet from the previous times interest was calculated.

Another way of saying compounded is two things added together or something made bigger. This means that when compounded the interest is made bigger.

Compound interest is calculated more often than simple interest, sometimes daily. In principle it could be calculated every second! A compounded interest rate will generally be higher than the equivalent quoted interest rate using simple interest. Sometimes a lot higher. Banks usually quote the base interest rate and not the total compounded rate which you actually pay.

I am going to use “powers” in this definition. A power is simply when a number is multiplied by itself by the number of times specified in the power. For example 2 to the power of 3, which can be written as 2 x 2 x 2 (= 8) or in short hand as 2^3, which is the same as 2 x 2 = 4 and then that answer, 4 x 2 = 8. Technically this shorthand is only used in software packages like Microsoft Excel, the formal way to write a power is by writing a small superscript of the “power” to the top right hand side of the the number you are taking to the power, as you can see in the figure drawn below.  When powers are used numbers can get big pretty fast – so when interest is calculated this way it can have quite an effect on the amount you end up paying on your debt or receiving on your savings.

If I borrow $1, and the interest rate is 10% p.a. but this time compounded daily. In the formula for compound interest (see diagram bellow), the interest rate, r = 10% or 0.1, the number of times compounded in the year or period, n = 365 days, the years or period, m = 1 year.

6DA3886D-E1D0-4C09-8265-CB16FA2AE397 1

In the formula, n and m can refer to days, years, months, quarters, half-years or really any break down of a year. Interest rate, r is always a percentage.

At the end of one year I now have to pay $1.105.

Total repayment = ( 1 + 0.1/365 ) ^ (365 x 1)

= 1.00027397 ^ (365 x 1)

= $ 1.105

By compounding every day, the 10% interest rate is actually higher than 10% after 1 year. I am actually paying 10.5% interest.

This means the effective annual interest rate of 10% p.a compounded daily, is 10.5%.

If you have a bank account that pays interest, you want it calculated an paid as often as possible to get the highest possible interest on your savings. So you can earn interest on the interest you receive.

Most credit card interest is calculated daily. Interest is often also added to the account balance daily so you are quickly charged interest on your interest. This is why credit card debt can get so big so quickly.

I really wouldn’t recommend getting a credit card unless it’s a low-to-zero annual fee and low interest card. It’s much better to save up for what you need, that way you don’t pay any interest and best of all the bank actually pays you interest on your savings (if you are lucky enough to live in a country where interest rates are not zero that is!). Of course everyone’s circumstances are different, that’s just my own personal preference. Unfortunately sometimes it is difficult to pay for large cost items without a credit card because some retailers don’t like to accept large cash payments or a prevented by law from accepting such payments. For those types of purchases I do use a low interest rate, low fee credit card and pay the money back onto my credit card balance almost right away out of my savings so that I am not in any debt and do not owe large amounts of interest (if any).

Studying at Masters level

Last year I decided to go back to university to study a Masters of Economics after several years working as a Teaching Assistant. At first it was really overwhelming. There is so much to read, write and think about and many new concepts to get my head around. It’s been really interesting and it’s been rewarding.

One of of the challenges I faced was learning how to sit and exam again. I hadn’t sat for a written exam since mid 2012 when I completed my Bachelors degree in science. I was incredibly nervous for the first few exams I sat. In one exam I ran out of time because I was too slow and being very careful. I remember in 2012 being so happy, thinking I would never sit another university exam again. How wrong I was!

I’m happy to finally be studying economics in depth rather than just having a layman’s interest.  I studied a little economics in my undergraduate degree but wasn’t able to do as much as I would have liked. Previously the subjects I took were in Political Economy and economics for project managers, like cash flow (future value, present value) calculations. I studied economics in high school and I had a great teacher who was great at explaining concepts. I will always remember those classes.

Now I can study topics that really interest me like macroeconomics. It’s also good to go back and relearn all the math I’d half forgotten! Learning it a second time has also filled up many of the little holes in my knowledge that were present the first time I studied university math. I’m still teaching, so it’s also good to share new tricks I have learned for the topics I do use regularly with my students who might be struggling.

I’ve just got through my mid semester exams for this semester but I’m feeling positive about the rest of the year ahead.