What is compound interest? This post answers this question, as well as other frequently asked questions on the topic, such as how you can compute it, how you can use it to prepare for your retirement, and how to make wiser financial decisions.

**RELATED: Roth IRA Interest Rates: How Does Your Money Grow?**

In this article:

- What Is Compound Interest?
- What Is an Amortization?
- When Is Compound Interest Used?
- Do Compound Interests Offer Benefits for Investors?
- Can Compound Interests Help in Planning for Retirement?
- Why Is Compound Interest Important?
- How Is Compound Interest Calculated?

## Answers to Frequently Asked Questions About Compound Interest

### What Is Compound Interest?

There are two ways to compute for interest:

- Simple
- Compound

**Simple Interest Method **

Under the simple interest method, computed interest **isn’t added back to the original principal amount**, which keeps the computed interest for succeeding periods **constant**. This is assuming there are no changes to the principal amount.

**Compound Interest Method **

Under the compound interest method, also called compounding interest, computed interest **is added to the outstanding principal amount**. This can result in **bigger** computed interest in the succeeding periods, assuming no changes in the principal amount.

Albert Einstein once said that compound interest was the 8th wonder of the world.

According to him, those who can answer “what is compound interest?” and understand it, *earn* it. On the other hand, those who don’t understand it end up *paying* it.

### What Is an Amortization?

A person who borrows money will be charged interest on a regular basis until the entire debt is paid off. Depending on the agreement with the creditor, a person can pay off the debt in one **lump sum (principal + interest)** at an agreed upon date in the future or through **installment payments (amortizations)**.

**Amortization Payments**

When paying a loan through amortization, a person pays a **specific** amount of money every month.

- Part of that amount goes toward the interest due on the outstanding amount of the loan
- The remaining amount goes toward payment of the outstanding or principal amount

After an amortization payment for a specific period, e.g., for the month, the outstanding amount owed is reduced, which is the basis for computing interest for the next amortization period. Because of the reduced principal amount, the interest for the next amortization period is lower and more of the payment amount can be applied to the principal amount.

### When Is Compound Interest Used?

However, when a person **misses** an amortization payment, the interest due for that missed payment is **compounded**, (i.e. added to the outstanding amount), which makes the principal amount used for computing the next period’s interest bigger. As a result, interest for the next period is bigger than the previous periods’ instead of smaller.

When a person isn’t able to pay amortization payments on a regular basis, the total amount owed **grows at a faster rate each time**. This is because, for every missed payment, creditors will add interest back to the outstanding amount, resulting in bigger interest for the succeeding periods.

This is what Einstein probably meant when he said those who don’t understand what is compound interest end up paying it.

### Do Compound Interests Offer Benefits for Investors?

When it comes to investments, compound interest can be a person’s best friend. This is because it can help make money grow at a faster rate compared to simple interest.

For example:

Let’s say a person wants to invest **$1,000** and has two investment options: to use simple or compound interest. Let’s say his investment choice is a **certificate of deposit (CD) **in a local bank, which is a deposit account that earns a **fixed** amount of interest for a specific period of time.

**Simple Interest Scenario **

Under a simple interest scenario, he places **$1,000 in a six-month CD at an annual rate of 2%**. At the end of one year, his CD earns** $20**, which he transfers to a non-interest bearing account.

**Interest for the 1 ^{st} Year** = $1,000 X 2%

**Interest for the 1 ^{st} Year** = $20

He re-invests the original $1,000 for a second year and a third year at the same rate. Each year yields **$20** in interest, bringing total interest for three years to **$60 and a total value of $1,060**.

**Compound Interest Scenario **

Under a compounded interest scenario, he does the same except that he reinvests the interest together with the original principal amount. This means he reinvests a bigger amount every time.

During the first year, he earns **$20** in interest, like in the simple interest method. But for the second year, he reinvests the $20 interest together with the original $1,000 principal amount, which increases the total principal amount to **$1,020**.

**Interest for 2 ^{nd} Year =** $1,020 X 2%

**Interest for 2 ^{nd} Year =** $20.40

If he reinvests the interest together with the principal for a 3^{rd} year:

**Interest for 3 ^{rd} Year =** $1,040.40 X 2%

**Interest for 3 ^{rd} Year =** $20.81

### Can Compound Interests Help in Planning for Retirement?

People who are planning for retirement (or financial planners helping them out) can also use compound interest in making important financial plans and decisions. They can use compound interest to estimate the **cost of living after retirement**, which becomes the benchmark in terms of how much money a person needs to save for retirement.

Inflation is the main reason why the cost of living after retirement is higher in the future. People who plan financially for their retirement years use inflation as a benchmark to estimate their future cost of living.

**Inflation Definition: **Inflation refers to the rate at which the cost of basic goods and services increases every year. If the government published that the inflation rate for January is 3%, this means the cost of living last January was 3% higher than the previous January.

### Why Is Compound Interest Important?

Learning about compound interest can help a person make better financial decisions to optimize their chances of achieving their financial goals. In particular, this can help in:

- Maximizing returns on investment
- Minimizing the likelihood of personal bankruptcy

A person who understands how compound interest works can evaluate investment opportunities wisely. More than just the rate of return on investments, compounding frequency can also help determine which investments are superior.

A person who understands how compounding interest works will be able to clearly see the ramifications of not being able to make timely amortization payments on debts. In particular, people will clearly see how fast debt can grow because of compounding, which can put them at risk for bankruptcy and inability to prepare for retirement.

In Einstein’s words, the person who understands compound interest earns it, while the person who doesn’t, pays it.

**RELATED: Return On Investments Formula | How To Calculate ROI**

### How Is Compound Interest Calculated?

To calculate compound interest, including the principal, this is the compound interest formula:

Where:

FV = Future Value (principal + compounded interest);

P = Principal Amount;

r = Growth Rate, e.g., interest, rate of return, inflation rate;

n = Annual Compounding Frequency, e.g., number of times compounded annually; and

t = Number of years.

For example, the compounded interest on a 5-year CD with a rate of 2% and compounded annually would be:

P = $1,000

r = 2% or 0.02

n = 1 (annual compounding)

t = 5 years

To calculate compound interest, including principal, substitute the figures in the compound interest formula:

The simple interest method will yield a total of only **$100** for five years because it keeps annual interest fixed. Total future value amounts are only **$1,100** compared to **$1,104.08** via compounding.

**Sample Scenario:**

Financial planners and those planning for retirement can also use compounding to estimate the future cost of living upon retirement. Let’s say the inflation rate over the last 20 years averages 5%, a person estimates his current annual cost of living at $30,000, and that he plans to retire in 20 years.

P = $30,000

r = 5% or 0.05

n = 1 (annual)

t = 20 years

This person will need to have $79,598.93 for the first year of retirement. Afterward, he’ll need to compound annual costs of living for succeeding retirement years to estimate total retirement cost.

Assuming all things equal, compounding more frequently will give a higher future value and vice-versa. Consider three investment options: A, B, and C.

All three investments give a 5% annual rate of return for 10 years. The only difference is that Investment A compound returns annually (n=1), Investment B semi-annually (n=2), and Investment C quarterly (n=4).

As the calculations validate, compounding more frequently results in a higher compounded future value. Given all things equal, choosing an investment option with the highest compounding frequency will yield the highest actual return.

When it comes to making wise long-term financial decisions, people need to know the answer to “what is compound interest?” Compound interest offers several benefits for investors and those who are planning for their lives after retirement alike.

Additionally, people who take out loans can also benefit from learning about this since it’ll help them understand the consequences of missed amortizations. Whatever the case may be, understanding more about compound interest helps people make better financial decisions.

**Have you had any experience with compound interest? What are some of the things you find confusing about it? Let us know in the comments section below.**

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