Simple vs compound interest: What is the difference?
Interest is the cost of borrowing money, where a fee is paid to a lender in exchange for a loan. Interest is usually expressed as a percentage, known as an interest rate.
For example, if you’re taking out a loan from the bank, they will add the interest (which is calculated over a set period of time) to the overall loan amount until you pay it all back. This is how the bank makes money.
However, interest can also work in your favour, as in the case of savings accounts and term deposits. With these you are essentially lending money to the bank, who will pay you the interest you accrue after a set period of time.
In both of these cases, the type of interest charged can be simple or compounded interest. So, what are the differences? Which is better? Is there even a better option? Moreover, how can you calculate the interest you’ll pay or receive? Let’s find out:
What is simple interest?
Simple interest is interest calculated on the original amount of a loan or the original contribution to a savings account, also known as the ‘principal’ amount.
It’s best understood in relation to compound interest, which we’ll get to later.
How is simple interest calculated?
Simple interest is calculated using the following formula:
A = P (1 + Rt)
- A is the total amount after interest is added (principal + interest)
- P is the principal amount (the original loan or deposit)
- I is the interest amount
- R is the rate of interest (calculated in decimal form)
- t is the time period
As an example, we’ll look at a starting amount (principal) of $10,000, with an interest rate of 5 per cent per annum, over a three year period.
- A = P + I
- P = $10,000
- I = ?
- R = 0.05 (or, 5 per cent, divided by 100)
- t = 3 years
Where $11,500 is the total amount you would pay on a personal loan of $10,000, with an interest rate of 5 per cent per annum over a three year period, we can deduce that you would be paying an additional $1,500 in simple interest as monthly repayments are made.
What is compound interest?
As opposed to simple interest, where the interest is paid at the end of a specific period of time, compound interest builds upon the principal amount. In other words, it snowballs.
You could have a daily, monthly, quarterly, or even yearly compounding interest rate, depending on the kind of financial product you’re dealing with.
How is compound interest calculated?
Compound interest is calculated using a compound interest formula, which can change depending on the compounding frequency.
A = P x (1 + R)^n
- A is the total amount after interest is added (principal + interest)
- P is the principal amount (the original loan or deposit)
- I is the interest amount
- R is the rate of interest (calculated in decimal form)
- n is the number of time periods
How is monthly compound interest calculated?
To calculate monthly compound interest, like those used in many savings accounts, you’ll have to use a formula which divides the interest rate by twelve months.
A = P x (1 + R/12)^n
For instance, when you take our previous example of a rate of 0.05 (5%), you would divide that by 12 months to get 0.00417 (rounded up). Then you’ll need to put it to the power of 36 months, rather than three years because it compounds monthly.
If this feels all too much like a high school maths lesson, you’re in luck because Mozo offers a compound interest calculator, which should help clear up any confusion you might have.
Which is better: simple or compound interest?
The answer all depends on if you’re the borrower (as in the case of a personal loan or home loan) or the lender (as in the case of a term deposit or savings account).
In the table below, we compare the same principal amount as interest is applied to it, using simple, compound, and monthly compound interest.
We start with a principal of $10,000, with an interest rate of 5 per cent (0.05) over a three year period. You’ll notice that the interest (I), when compounded, grows much quicker over the same period of time - especially when it’s calculated on a monthly basis.
In short, simple interest is better if you’re borrowing and compound interest is better if you’re investing.
However, it’s good to be aware that banks know this too, meaning that they will often adjust their rates to account for the advantages of compound interest. That being said, compound interest will often grow your savings or investment at a faster pace than simple interest.