Compound Interest: Explanation, Formula, & Calculation

Compound interest is a simple idea, but can be a little tricky to wrap your head around. In this article, we’ll take a look at the concept of compound interest, explain why it is such a powerful force for investors, and how you can use it to your advantage.

Compound Interest Explanation

Let’s start with the basics. When you put money into an investment, you will generally receive extra money each year as a return on your investment. This return is normally expressed as a percentage of the amount of money you invested in the first place – called the “principal”.

Let’s say you invested $1,000, and the return you receive is 10% – this means that at the end of the first year, you will have your original $1,000, plus an extra 10%. That’s $1,100.

Next year, your money will be reinvested, but now there is more in the account. A higher principal, in other words. If your returns stay the same at 10%, the next year you will receive 10% on the new amount.

10% of $1,100, which is $110 – $10 more than the year before. This means that at the end of the second year, you’ll have $1,210. 

This process will continue each year (or however often your investment is “compounded”). By the end of the 10th year, you’ll have $2,594, more than double your initial savings (without adding any more of your own money after your initial investment). You can thank compound interest for that.

Your investment would grow like this:

At a basic level, you can think of compound interest as “interest on interest”. As you receive returns on your investments, your principal will continue to grow, and you will receive higher returns every year, even if you don’t invest any more money.

Compound Interest Formula

There are a number of ways of working out the returns you can realize from compound interest. The simple way is the one we’ve presented above – for each year, you can complete the same basic sum, and repeat this to work out how much money you will have in ten years, twenty years, or when you retire.

There are easier ways to get to the same number, though. The standard compound interest formula is:

A = P(1+r/n)^nt

• P is the principal (the starting amount)
• r is the annual interest rate, which is written as a decimal
• n is the number of times the interest compounds each year
• t is the time, or total number of years
• A is the total amount you will wind up with at the end of the timeframe

For those of you who don’t use math on a regular basis, this formula might be a little daunting. But don’t worry – if you are unsure how to use it, you can use one of the many online calculators to figure out how much interest will accrue and how compounding can impact your savings or debt.

If you have some basic math, though, even a quick look at the formula and you’ll be able to see some key points about how compound interest works.

Whether you’re saving or borrowing money, you may already know the amount you’ll start with (P) and your timeframe (t). As a result, there are two variables to consider as you compare your options—the interest rate (r) and compounding frequency (n). 

The impact of a higher or lower interest rate is fairly straightforward. A higher rate means more interest gets added each cycle.

But the compounding frequency can also have a huge effect on the amount of money you will receive (or will owe) at the end of the period – a higher compounding frequency (say once a month, instead of once a year) can increase you gains (or debt) considerably.

Can Compound Interest Make You Rich?

Though the idea of compound interest is straightforward, it’s effects can be very surprising. Compound interest is basically a way of expressing exponential growth, and we’ve all had personal experience of how powerful that can be during the recent pandemic.

This means that compound interest can be a great tool for an investor, and a huge pain for a borrower. Compound interest is one of the primary reasons why it can be so hard to pay off credit card debt – because credit card companies charge interest on your debt, and then interest on that interest, it can be easy to get into trouble when it comes to borrowing in this way.

If you are on the other side of the equation, though, compound interest is a great way of building wealth. Choose an investment with a high return rate, and one that compounds regularly, and keep your money in it. As your money passes through multiple compounding cycles, you will quickly see significant growth.

Is Compound Interest Haram?

Though authorities are a little split on this issue, there is a broad consensus that profiting from compound interest is haram for Muslims. 

This is because the Muslim line on fixed-income investments is fairly clear. Simple and compound interest is forbidden. That includes interest-bearing securities such as bonds, mortgages, debentures, guaranteed investment certificates, savings accounts – anything that gives a guarantee of principal or fixed rate of return.

That could make saving for retirement difficult for devout Muslims, because the benefits of compound interest are denied to them. Muslims have a wide variety of halal investing options they can invest in but not compound interest.

Read: Halal Investing: A Beginner’s Guide

A Powerful Tool

As with many concepts in investing, compound interest can be a little difficult to grasp at first. However, once you understand the principle that is at work here, it’s easy to use it to maximize the gains you can make from your investments.

The key to taking advantage of compound interest is to leave your money to work through many compounding cycles, and grow in value at each stage, rather than succumbing to the temptation to take your profits at an earlier stage.