Interest is defined as the cost of borrowing money, as in the case of interest calculated on the loan balance. Conversely, interest can also be paid on deposit money, as in the case of a certificate of deposit. Interest can be calculated in two ways:simple interestthecommon interest.

**Simple interest**calculated atMr, i.e. the initial amount of the loan.**Common interest**isis calculatedon the amount of principal and accumulated interest of previous periods, and therefore can be considered "interest on interest".

There can be a big difference in the amount of interest paid on the loan if the interest is calculated on a compound rather than a simple basis. On the bright side, the magic of interest can work in your favor when it comes to your investments and can be a powerful factor in wealth creation.

Whilesimple interest and compound interestare basic financial terms, being fully familiar with them can help you make more informed decisions when taking out a loan or investing.

## A simple type of interest

The formula for calculating simple interest is:

$\begin{aligned}&\text{Simple Interest} = P \times i \times n \\&\textbf{where:}\\&P = \text{Principal} \\&i = \text{Interest Rate} \\ &n = \text{Loan Term} \\\end{settled}$Simple interest=Pi×and×nwhere:Pi=Mrand=Interest raten=Loan conditions

So, if simple interest is charged at 5% on a $10,000 loan taken out over three years, then the total amount of interest paid by the borrower is calculated as $10,000 x 0.05 x 3 = $1,500.

Interest on this loan is paid at a rate of $500 per year, or $1,500 over the three-year term of the loan.

## Compound Interest Type

The formula for calculating compound interest per year is:

$\begin{aligned} &\text{Compound interest} = \big ( P(1 + i) ^ n \big ) - P \\ &\text{Compound interest} = P \big ( (1 + i) ^ n - 1 \big ) \\ &\textbf{where:}\\ & P= \text{Principal}\\ &i = \text{Interest in percentage} \\ &n = \text{Number of compounding periods per year} \ \ \end{aligned}$Common interest=(Pi(1+and)n)−PiCommon interest=Pi((1+and)n−1)where:Pi=Mrand=Interest in percentage valuesn=Number of training periods in a year

Compound interest = total amount of principal and interest in the future (orfuture value) reduced by the current capital, the so-calledpresent value(PV). PV is the present value of a future cash sum or flowThe cash is flowingregarding the aboverate of return.

Continuing with the simple interest example, what would the amount of interest be if it were calculated on a compounding basis? In this case it would be:

$\begin{aligned} \text{Kamata} &= \$10.000 \big( (1 + 0,05) ^ 3 - 1 \big ) \\ &= \$10.000 \big ( 1,157625 - 1 \big ) \\ &= \$1.576,25 \\ \end{poravnano}$Interesting=10 USD,000((1+0,05)3−1)=10 USD,000(1,157625−1)=$1,576,25

Although the total interest paid over the three years of this loan is $1,576.25, unlike simple interest, the interest amount is not the same for all three years because compound interest also takes into account accrued interest from previous periods. The interest payable at the end of each year is shown in the table below.

Year | Initial state (P) | Interest rate 5% (I) | Final Balance (P+I) |

1 | $10,000.00 | 500.00 dollars | $10,500.00 |

2 | $10,500.00 | $525.00 | $11,025.00 |

3 | $11,025.00 | $551.25 | $11,576.25 |

Overall interest | 1576.25 dollars |

1:52

#### SEE: What is Compounding?

## Billing periods

When calculating compounding, the number of accounting periods makes a significant difference. Generally, the longer the number of billing periods, the higher the compounding amount. Thus, for each credit of $100 for a certain period, the amount of interestcalculate10% p.a. will be lower than interest calculated at 5% semi-annually, which in turn will be lower than interest calculated at 2.5% quarterly.

In the formula for calculating compound interest, the variables "i" and "n" must be adjusted if the number of compounding periods is greater than once a year.

That is, inside the brackets, "i" or the interest rate must be divided by "n", the number of compounding periods per year. Outside the parentheses, "n" must be multiplied by "t", the total length of the liner.

Therefore, for a 10-year loan at 10%, where interest is calculated semi-annually (number of calculation periods = 2), i = 5% (i.e. 10% ÷ 2) and n = 20 (i.e. 10 x 2).

To calculate the total value with compound interest, you would use this equation:

$\begin{aligned} &\text{Total value with compound interest} = \Big( P \big ( \frac {1 + i}{n} \big ) ^ {nt} \Big ) - P \\ &\text {Compound interest} = P \Big ( \big ( \frac {1 + i}{n} \big ) ^ {nt} - 1 \Big ) \\ &\textbf{where:} \\ &P = \text{ Main} \\ &i = \text{Interest in percentages} \\ &n = \text{Number of calculation periods per year} \\ &t = \text{Total number of years for investment or loan} \\ \end {even out}$TotalValuewithCompoundInterest=(Pi(n1+and)nt)−PiCommon interest=Pi((n1+and)nt−1)where:Pi=Mrand=Interest in percentagesn=Number of mixing periods in a yeart=Total number of years for investment or loan

The following table shows the difference the number of upgrade periods can make over time for a $10,000 loan taken out over a 10-year period.

Agreement frequency | Billing period number | Values for i/n and nt | Overall interest |

Per year | 1 | i/n = 10%, nt = 10 | $15,937.42 |

Half a year | 2 | i/n = 5%, nt = 20 | 16.532,98 $ |

Quarterly | 4 | i/n = 2,5%, nt = 40 | 16.850,64 $ |

Every month | 12 | i/n = 0,833%, nt = 120 | $17,059.68 |

## Other concepts of interest in compound interest

### Time value of money

Since money is not "free" but has a cost in terms of interest payable, it follows that a dollar today is worth more than a dollar in the future. This concept is known asTime value of moneyand is the basis for relatively advanced techniques such as e.gdiscounted cash flow(DFC) analysis. The opposite of stacking is known asdiscounting. The discount rate can be thought of as the inverse of the interest rate and is the factor by which the future value must be multiplied to obtain the present value.

The formulas for obtaining future value (FV) and present value (PV) are as follows:

$\begin{aligned}&\text{FV}=PV\times\left[\frac{1+i}{n}\right]^{(n\times t)}\\&\text{PV}=FV \div\left[\frac{1+i}{n}\right]^{(n\times t)}\\&\textbf{where:}\\&i=\text{Interest in percentages}\ \ &n =\text{Number of billing periods per year}\\&t=\text{Total number of years for investment or loan}\end{aligned}$FV=PiV×[n1+and](n×t)PV=eatV÷[n1+and](n×t)where:and=Interest in percentage valuesn=Number of mixing periods in a yeart=Total number of years for investment or loan

### Rule 72

TheRule 72calculates the approximate time it takes an investment to double at a given rate of return or interest "i" and is given by the expression (72 ÷ i).It can only be used for an annual calculation, but it can be very helpful in planning how much money you can expect in retirement.

For example, an investment that has an annual rate of return of 6% will double in 12 years (72 ÷ 6%).

An investment with an annual rate of return of 8% will double in nine years (72 ÷ 8%).

## Compound Annual Growth Rate (CAGR)

Thecompound annual growth rate(CAGR) is used for most financial applications that require the calculation of a uniform growth rate over a period.

For example, if your investment portfolio grew from $10,000 to $16,000 over five years, what is the CAGR? Essentially, this means that PV = $10,000, FV = $16,000, and nt = 5, so the variable "i" must be calculated. Using a financial calculator orExcel spreadsheet, it can be shown that i = 9.86%.

Note that under the cash flow convention, your initial investment (PV) of $10,000 is shown with a negative sign, as it represents an outflow of funds. PV and FV must necessarily have opposite signs to solve for "i" in the above equation.

## Real life applications

CAGR is used extensivelyto calculate returns over periodsfor stocks, mutual funds and investment portfolios. CAGR is also used to determine whether a mutual fund manager or portfolio manager has outperformed the market rate of return over a period of time. For example, if the market index provided total returns of 10% over five years, but the fund manager achieved annualized returns of only 9% over the same period, then the fund manageris not performed adequatelyThe market.

CAGR can also be used to calculate the expected growth rate of investment portfolios over long periods, which is useful for purposes such as saving for retirement. Consider the following examples:

- A risk-averse investor is happy with a modest annual rate of return of 3% on his portfolio. Therefore, their current portfolio of $100,000 will grow to $180,611 after 20 years. Conversely, a risk-tolerant investor who expects a 6% annual rate of return on his portfolio will see $100,000 grow to $320,714 after 20 years.
- CAGR can be used to calculate how much needs to be saved to save for a particular goal. A couple who would like to save $50,000 over 10 years for a down payment on a condo would need to save $4,165 per year assuming a 4% compound annual rate of return (CAGR) on their savings. If they are willing to take on additional risk and expect a CAGR of 5%, then they should save $3,975 per year.
- CAGR can also be used to show the virtues of investing earlier rather than later in life. If the goal is to save $1 million by retirement at age 65, based on a 6% CAGR, a 25-year-old would need to save $6,462 per year to reach that goal. On the other hand, a 40-year-old would need to save $18,227, or nearly three times as much, to reach the same goal.

## Additional considerations of interest

Make sure you know it rightannual rate(APR) on your loan, as how it's calculated and the number of upgrade periods can affect your monthly payments. Although banks and financial institutions have standardized methods for calculating the interest payable on mortgages and other loans, the calculations may differ slightly from one country to another.

The payment can work in your favor when it comes to your investments, but it can also work in your hand when paying off the loan. For example, paying off half of your mortgage twice a month, rather than making the full payment once a month, will shorten your repayment period and save you a significant amount of interest.

The payment can be against you if you have loans with very high interest rates, such as credit card or department store debt. For example, a $25,000 credit card balance with an interest rate of 20%—compounded monthly—would result in a total of $5,485 in interest over a year, or $457 per month.

## The bottom line

Make the magic of the combination work for you by investing regularly and increasing your loan repayment frequency. Learning the basic concepts of simple and compound interest will help you make better financial decisions, saving you thousands of dollars and increasing your net worth over time.

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## FAQs

### What is simple vs compound interest answers? ›

Generally, simple interest is an annual payment based on a percentage of the saved or borrowed amount, also called the annual interest rate. Compound interest is interest earned not just based on the saved or borrowed amount, but also on the interest already earned so far.

**What major difference between compound interest and simple interest is that simple interest? ›**

The difference between simple interest and compound interest is the way the interest accumulates. **Simple interest accumulates only on the principal balance, while compound interest accrues to both the principal balance and the accumulated interest**.

**What is an example of simple and compound interest? ›**

Sol: **The Simple Interest after three years @ 10% is 30%.** **The Compound Interest after 3 years @ 10% will be 1.1 × 1.1 × 1.1 = 1.331** Cumulative rate of Interest is 33.1%. Here, the difference after 3 years is 3.1% and in the question it is given to be Rs. 930.

**What is the simple definition of compound interest? ›**

Compound interest is **when you earn interest on both the money you've saved and the interest you earn**.

**What is an example of a simple interest? ›**

Simple Interest

Interest, in its most simple form, is calculated as a percent of the principal. For example, **if you borrowed $100 from a friend and agree to repay it with 5% interest, then the amount of interest you would pay would just be 5% of 100: $100(0.05) = $5**.

**What is an example of a compound interest? ›**

Compound interest definition

For example, **if you deposit $1,000 in an account that pays 1 percent annual interest, you'd earn $10 in interest after a year**. Thanks to compound interest, in Year Two you'd earn 1 percent on $1,010 — the principal plus the interest, or $10.10 in interest payouts for the year.

**Are bank loans simple or compound interest? ›**

Hence, Banks use **both simple interest and compound interest**.

**Are car loans simple interest? ›**

Key Takeaways. **Interest on an auto loan is calculated using simple interest**, not compound interest, meaning the interest doesn't earn interest. Interest on a car loan is often front-loaded so that early payments pay more toward interest and less toward the paydown of the principal loan balance.

**Is my interest simple or compound? ›**

Simple Interest | Compound Interest |
---|---|

Charged on the principal yearly. That interest is then added to the principal balance | Charge on both the principal and interest accrued |

Always calculated annually | Calculated at various frequencies, including daily, monthly, quarterly or annually |

**Is house interest simple or compound? ›**

Loans: Student loans, personal loans and mortgages all tend to calculate interest based on a compounding formula. Mortgages often compound interest daily. With that in mind, the longer you have a loan, the more interest you're going to pay.

### What is the best definition of a compound? ›

(KOM-pownd) In science, **a substance made from two or more different elements that have been chemically joined**. Examples of compounds include water (H2O), which is made from the elements hydrogen and oxygen, and table salt (NaCl), which is made from the elements sodium and chloride.

**How do you find simple interest? ›**

To calculate simple interest, multiply the principal amount by the interest rate and the time. The formula written out is "Simple Interest = Principal x Interest Rate x Time." This equation is the simplest way of calculating interest.

**How do you explain compound interest to a child? ›**

'Compound interest' simply means **earning interest on your savings, and also, eventually, on the interest that those savings earn**. The earlier your child begins to save, the more compound interest they'll earn.

**What are two types of interest? ›**

Two main types of interest can be applied to loans—**simple and compound**. Simple interest is a set rate on the principal originally lent to the borrower that the borrower has to pay for the ability to use the money. Compound interest is interest on both the principal and the compounding interest paid on that loan.

**What is simple interest for dummies? ›**

Simple interest is **the interest charge on borrowing that's calculated using an original principal amount only and an interest rate that never changes**. It does not involve compounding, where borrowers end up paying interest on principal and interest that grows over multiple payment periods.

**Why is compound interest better? ›**

Compound interest **makes your money grow faster because interest is calculated on the accumulated interest over time as well as on your original principal**. Compounding can create a snowball effect, as the original investments plus the income earned from those investments grow together.

**What are 5 examples of interest? ›**

They can include hobbies, sports, artistic expression, leisure activities, volunteering, cultural activities, spiritual practices, traditional activities, learning pursuits, and personal development. Common personal interests include: Crafts, such as sewing, embroidery, scrapbooking. Cooking and baking.

**Are there 2 formulas for simple interest? ›**

Summary. This topic uses two formulas: **Interest=Principal×Rate×TimeI=PRTAmount=Principal+InterestA=P+I** Principal is your starting amount of money.

**What are the types of simple interest problems? ›**

What are the types of simple interest? While the formula for calculating the simple interest remains the same, there are two types of it: **ordinary and exact**. The only difference is the usage of time in both categories.

**What are 3 examples of a compound? ›**

**Examples of Compounds**

- Water (H
_{2}O) - Hydrogen peroxide (H
_{2}O_{2}) - Carbon monoxide (CO)
- Carbon dioxide (CO
_{2}) - Methane (CH
_{4}) - Sodium chloride (NaCl)
- Glucose (C
_{6}H_{12}O_{6}) - Sodium bicarbonate (NaHCO
_{3})

### Is fixed deposit interest simple or compound? ›

How is the interest on a bank FD calculated? Usually, **the interest for FD with a period of 6 months or less is calculated at simple interest**. Compounding of interest is done for FDs with a term period of more than 6 months. When going for monthly interest payout, banks mostly calculate interest on discounted rates.

**Are home equity loans simple or compound interest? ›**

Most lines of credit, even home equity lines of credit, use a **simple interest** method as opposed to compounding interest.

**Are credit cards simple or compound interest? ›**

Most credit card issuers will **compound interest charges daily**. In other words, the issuer will add interest charges each day based on your balance from the previous day, then use that to determine your total interest due each month. Accounting for compounding manually would be extremely time-consuming.

**What are the disadvantages of simple interest? ›**

Simple interest has the disadvantage that **if the interest rate is high, the borrower will pay more**. Furthermore, if the repayment period (years) is greater, the borrower will pay more.

**What is the fastest way to pay off a simple interest loan? ›**

Pay off your debt and save on interest by **paying more than the minimum every month**. The key is to make extra payments consistently so you can pay off your loan more quickly. Some lenders allow you to make an extra payment each month specifying that each extra payment goes toward the principal.

**What is the rule of 72 that is related to saving? ›**

Do you know the Rule of 72? It's an easy way to calculate just how long it's going to take for your money to double. Just **take the number 72 and divide it by the interest rate you hope to earn**. That number gives you the approximate number of years it will take for your investment to double.

**What is the magic of compound interest? ›**

Compound interest is when the interest you earn on a balance in a savings or investing account is reinvested, earning you more interest. As a wise man once said, “Money makes money. And the money that money makes, makes money.” Compound interest **accelerates the growth of your savings and investments over time**.

**What do you called to an interest based on a 360 day year? ›**

**Actual/360, also known as the 365/360 rule**, is the method most commonly used by banks to calculate interest accrual. You get it by dividing the annual interest rate by 360 to get a daily interest rate.

**Is rent a compound interest? ›**

**The principle of compounding can also be applied to rental income**. A lease agreement with a built-in 4% rent increase each year is another example of compounding. If the rent in year one is $1,000 per month, it would be $1,040 in year two.

**Is real estate simple interest? ›**

**Simple interest works the same in real estate as it does for other loan types**. Your monthly payment will first cover your APR, which includes simple interest charges, and the remainder of your payment will contribute to paying off your principal balance.

### How is simple interest used in real life? ›

Simple interest is more advantageous for borrowers than compound interest, as it keeps overall interest payments lower. **Car loans, amortized monthly, and retailer installment loans, also calculated monthly**, are examples of simple interest; as the loan balance dips with each monthly payment, so does the interest.

**How do you identify a simple or compound sentence? ›**

**A simple sentence contains one independent clause.** **A compound sentence contains more than one**! Put another way: a simple sentence contains a subject and a predicate, but a compound sentence contains more than one subject and more than one predicate.

**Is water a simple compound? ›**

**Although the molecules of water are simple in structure (H _{2}O)**, the physical and chemical properties of the compound are extraordinarily complicated, and they are not typical of most substances found on Earth.

**What are 10 examples of compound sentence? ›**

**10 Compound Sentences in English**

- Our car broke down. ...
- They spoke to him in English, but she responded in Spanish.
- She goes to the beach, and she takes her cat.
- Although Michael reads novels, Joly reads comics.
- 5.As Alex was arriving to work, he realized he forgot his lunch.

**What are the types of compound? ›**

Compounds can be classified into two types, **molecular compounds and salts**.

**Is water a compound or a mixture? ›**

Water is **a compound** because it is made up of water molecules. There is no such thing as water atoms. Water molecules are made of hydrogen and oxygen atoms, in the definite proportion of two hydrogens for one oxygen.

**Which of the following is not a compound? ›**

Hence, the correct option is A i.e. **Ozone** is not a compound.

**How do you calculate compound interest? ›**

The compound interest formula is **((P*(1+i)^n) - P)**, where P is the principal, i is the annual interest rate, and n is the number of periods.

**How do you teach simple and compound interest? ›**

**So here are five possible ways we recommend explaining compound interest so it sticks with your students for life!**

- Tell a story. People are hardwired to remember stories. ...
- Do an activity. ...
- Make it practical. ...
- Play a game. ...
- Work a real-life problem.

**What grade do you learn compound interest? ›**

IXL | Compound interest | **7th grade** math.

### What is the difference between simple and compound interest quizlet? ›

What is the difference between simple and compound interest? Simple interest is interest payment is calculated on only the principal amount; whereas compound interest is interest calculated on both the principal amount and all the previously accumulated interest.

**Which best describes the difference between simple and compound interest quizlet? ›**

Which describes the difference between simple and compound interest? **Simple interest is paid on the principal, while compound interest is paid on the principal and interest accrued**.

**Are car loans simple or compound interest? ›**

Key Takeaways. Interest on an auto loan is calculated using **simple interest, not compound interest**, meaning the interest doesn't earn interest. Interest on a car loan is often front-loaded so that early payments pay more toward interest and less toward the paydown of the principal loan balance.

**Why compound interest is more powerful than simple interest? ›**

Compound interest causes your wealth to grow faster. It makes a sum of money grow at a faster rate than simple interest because **you will earn returns on the money you invest, as well as on returns at the end of every compounding period**. This means that you don't have to put away as much money to reach your goals!

**What is simple interest calculator? ›**

A simple interest calculator is **a utility tool that calculates the interest on loans or savings without compounding**. You may calculate the simple interest on the principal amount on a daily, monthly, or yearly basis.

**Is simple interest always greater than compound interest? ›**

**Compound interest is always lesser than simple interest when calculated on the same principal, time period and rate of interest**.

**How is compound interest different than simple interest quizizz? ›**

**Compound interest pays interest on your previous balance plus your previous earned interest; simple interest pays interest only on your original balance**.

**What is the key difference between simple interest and compound interest and how does this difference affect the effectiveness of each brainly? ›**

**Simple interest is based on the principal amount of a loan or deposit, while compound interest is based on the principal amount and the interest that accumulates on it in every period**. Since simple interest is calculated only on the principal amount of a loan or deposit, it's easier to determine than compound interest.

**What is an example of compound answer? ›**

2. Example Of Compounds. Example of compounds includes **water (H _{2}O), Hydrogen Peroxide (H_{2}O_{2})**, etc. You could see water's chemical formula, it says it has 2 atoms of Hydrogen combined with 1 atom of oxygen and in hydrogen peroxide, it has 2 atoms of hydrogen and two atoms of oxygen.

**Is home loan simple or compound? ›**

The important thing to note for Home Loan interest rate is that it is **compounded interest and not simple interest**. In other words, you don't pay interest only on the principal amount, but you pay interest on the principal amount plus the interest accrued.

### Is home loan interest compounded or simple? ›

**Compound interest** is the addition of interest to the principal sum of a loan – basically meaning that you pay interest on interest. Compound interest is standard practice when taking out a home loan.

**What uses compound interest? ›**

**To take advantage of the magic of compound interest, here are some of the best investments:**

- Certificates of deposit (CDs) ...
- High-yield savings accounts. ...
- Bonds and bond funds. ...
- Money market accounts. ...
- Dividend stocks. ...
- Real estate investment trusts (REITs)