What Is Compound Interest? Formula and How To Calculate

Let’s say you have $1,000 in a savings account that earns 5% in annual interest. In year one, you’d earn $50, giving you a new balance of $1,050. In year two, you would earn 5% on the larger balance of $1,050, which is $52.50—giving you a new balance of $1,102.50 at the end of year two.

Thanks to the magic of compound interest, the growth of your savings account balance would accelerate over time as you earn interest on increasingly larger balances. If you left $1,000 in this hypothetical savings account for 30 years, kept earning a 5% annual interest rate the whole time, and never added another penny to the account, you’d end up with a balance of $4,321.94.

What is compound interest?

How to calculate compound interest

Determining compound interest is a relatively easy process that follows a specific mathematic formula. The steps to calculating compound interest are:

The best formula for compound interest calculation is:

= [P(1+i)n]– P

= P[(1+i)n–1]

In this formula, “P” equals principal, “i” is the yearly interest rate in percentages, and “n” equals the number of annual compounding periods.

As an example, let us consider a five-year loan of $20,000 at an interest rate of 5% that compounds once a year. Using the formula, we can determine it will be: $20,000[(1 + 0.05)5 – 1] = $25,525.63

What is compound interest?

There are two distinct ways to calculate interest: compound and simple. Simple interest refers to a specific percentage of money that you earn each year based on the original principal amount that you invested. However, compound interest calculations are based on the amounts in all your accounts, even as they change and grow. In this way, compound interest can earn you what financial advisers call “interest on interest” and can contribute significantly to your success as an investor.

The easiest way to explain compound interest is to consider a practical example. For instance, let us suppose you invested $10,000 at 5% simple interest. This means that after the first year, $500 would be added to your account. In the second year, you would earn another $500, and the same would occur in the third year, the fourth year, and continuing.

However, this would change significantly if you used the compound method instead. If your investment earned you 5% of compound interest once a year, it would not have an obvious effect at first. Each year, you would receive the same $500 interest payment as you would if you used a simple interest calculation. But, in the second year, your 5% interest would be calculated based on your new balance of $10,500, instead of just your original $10,000. This would result in an interest payment of $525 for the second year which would then be added on to the principal when the time comes to calculate your interest for the third year.

What is a compound annual growth rate?

Compound annual growth rate, also called CAGR, is the rate of investment return necessary for an investment to increase from a beginning balance to its final balance if we assume the investor reinvested the profits once per year throughout the investment.

To determine the CAGR of an investment, you can follow three simple steps:

The formula for this calculation looks like this:

For example, if you wanted to know the annual growth rate of a $10,000 investment which resulted in an end value of $15,679 after five years, you would calculate the following equation: CAGR = (15,000/10,000)^(1/5)-1.

In this circumstance, the CAGR would be just over 0.084.

What is a compounding period?

The number of compounding periods you consider when calculating compound interest is very important. The compounding period is the span of time between the interest was last compounded and when it will be compounded again. The fundamental rule is that if you increase the number of compounding periods, you will also increase the regular amount of compound interest.

Because it is frequently recalculated, compound interest can increase investment returns considerably over time. A $100,000 amount that earns 5% simple interest would profit just $50,000 over the course of ten years. However, a compound interest rate of 5% on $10,000 would eventually result in $62,889.46 after the same interval.

Advantages of compound interest

Compound interest can be extremely beneficial if you can allow a significant amount of time for your investment to grow. Compound interest has the power to make a relatively small investment earn a large profit over a long period of time.

Compound interest helps your account funds increase quickly because the rate of growth is calculated based on the money you accumulate over the years in addition to the original principal amount. Compounding interest helps your money increase exponentially as your original investment and the profits that you have earned increase together.

As an example, lets say Jane saved $50 per month for 10 years in a savings account. If she does not invest it or earn interest from it, she will have $6,000 at the end of the 10 years. However, if she invests $50 per month for 10 years and earns 10% per year on her investment, she would have a final amount of $10,518. Therefore, she will have more than double her original amount.

Disadvantages of compound interest

One of the drawbacks of taking advantage of compound interest options is that it can sometimes be more expensive than you realize. The cost of compound interest is not always immediately apparent and if you do not manage your investment closely, making interest payments can actually lose you money.

Missing a regular interest payment by a day may mean that your rate decreases due to the compound interest being calculated before your payment is recorded. This could cost you a significant amount depending on the size of your regular payments. To avoid this, you will need to carefully time your monthly payments and stay on top of your payment schedule.

Another issue is that compound interest is designed to benefit lenders. The date for monthly credit card repayments is often purposefully set so you are encouraged to keep borrowing and therefore continue paying interest. To lower the amount of capital you owe, you can prioritize repaying interest plus a portion of the capital amount each month.

Compound interest example

To finish, we will look at a couple of examples of what compound interest calculations can look like in real life:

Annual compound interest example

Mr. Jackson decides to open his own flower shop. To fund his start-up costs, he makes an initial investment of $5,000 to be paid over three years. What will the value of the investment be after the three years if the investment earns a return of 10% compounded interest annually?

To calculate the value of the investment after a period of three years, we will need to use the annual compound interest formula, which is A = P (1 + r / m) mt.

In this example:

Now, we can calculate the future value (A) as follows:

In this example, Mr. Jacksons final amount after three years would be $6,655, which is a profit of $1,655.

Monthly compound interest example

Ms. Elliot receives $10,000 from her grandparents as a graduation gift. She decides to invest the original $10,000 for five years. We can find the value of the investment after the five years by calculating what the investment will earn at a 3% interest rate if compounded monthly.

To calculate the value of the investment after the period of five years, we will use the monthly compound interest formula: A = P (1 + r / m) mt

For this example:

Now, we can calculate the Future Value like this:

In this example, after five years, Ms. Elliot will have a final amount of $11,616. Her total profit will be $1,616.

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