Simple interest vs. compound interest
Interest is the cost of borrowing money, such as that charged on a loan. But it’s also the rate paid for your deposited money in various investments. In both cases, this interest is calculated in two distinct ways: simple and compound. It pays to understand the difference between the two.
What is simple interest?
Simple interest is calculated annually on a loan's principal or original amount. So, for example, after four years, a loan or investment of $30,000 with a 2.25 percent annual percentage rate (APR) would accrue $2,700 in interest. The interest rate can be fixed, depending on the company and product.
How does simple interest work?
To understand how simple interest works and is calculated, we need to take a look at the basic formula:
l = Prt
Here’s what the elements of the formula represent:
I = interest accumulated
P = initial principal balance
r = interest rate
t = number of elapsed time periods in years
So, to calculate how much you’ll pay in interest, you multiply the principal of $30,000 by the interest rate – expressed as 0.0225 (2.25 percent in decimal form) – and the number of years elapsed. In our example, that equals $2,700. So, you’d pay $32,700 over the four years, or the principal plus accrued interest.
What is compound interest?
Compound interest is a lot more complex and can generate much higher totals, because of how it’s calculated and what it includes.
It’s charged on both the principal and any interest that has accumulated.
Compound interest is also calculated more frequently than simple interest – daily, monthly or quarterly – and the rate can be variable, depending on the type of account.
How does compound interest work?
The way that compound interest works tends to make it a more expensive proposition. Take your credit card as an example. If it compounds interest daily, you’ll be paying the previous day’s interest plus the existing principal balance, so the amount you owe can grow quickly.
The flip side is that compound interest can work for you when investing.
If you invest early in a retirement plan and make regular payments, you will benefit from compounding interest over time. Interest payments are calculated on the existing principal and what you’ve already made through previous interest. So, the earlier you begin saving, the longer your investment will grow.
If you invest $10,000 at an annual interest rate of 3.875 percent, compound interest would, over a year, generate $394.45, giving you a total of $10,394.45.
Here’s the formula for calculating compound interest:
A=P[1+r/n]nt
This is what the elements of the formula represent:
A = Final amount
P = Initial principal balance
r = interest rate
n = number of times interest is applied per period
t = number of time periods elapsed in months or years
So, using our example, the formula shows a gain of $394.46 over one year.
We have a compound interest calculator you should check out if you want to see the impact time can have on your savings and investments.
Simple interest vs. compound interest
Whether you pay simple or compound interest will depend on what kind of loan or investment product you have.
Installment loans, like auto loans or mortgages, tend to use simple interest, meaning the amount of interest you pay decreases as your balance decreases.
Compound interest is typically used on savings accounts and credit cards. So, unlike simple interest, you accrue more interest as your loan continues. If you’re paying off credit card debt, this isn’t good news, but with a savings account, it certainly is.
Here’s an example to show you the difference between the two. You have a loan of $5,000 with a steady APR of 15.16 percent.
| Principal | APR | Principal and interest balance after one year [Simple] | Principal and interest balance after five years [Simple] | Principal and interest balance after one year [Compound] | Principal and interest balance after five years [Compound] |
|---|---|---|---|---|---|
| Principal | APR | Principal and interest balance after one year [Simple] | Principal and interest balance after five years [Simple] | Principal and interest balance after one year [Compound] | Principal and interest balance after five years [Compound] |
| $5,000 | 15.16 percent | $5,758 | $8,790 | $5,812 | $10,619.48 |
The table clearly shows how compound interest affects your payments as time passes. Compound interest accrues more quickly than simple interest, and if you’re borrowing, it can result in substantial additional costs. However, when you’re on the investing side of the equation, you will clearly benefit.
The bottom line
Get to grips with the differences between simple and compound interest, and you will be much better able to choose the right borrowing for your circumstances and understand how your investments and savings grow.
It’s best to seek an expert financial advisor who can help you understand your options and build a strategy that works.
Senior Content Writer
Rachel is a Senior Content Writer at Unbiased. She has nearly a decade of experience writing and producing content across a range of different sectors.