# Simple interest vs. compound interest (with calculations)

By Indeed Editorial Team

Published 12 April 2022

The Indeed Editorial Team comprises a diverse and talented team of writers, researchers and subject matter experts equipped with Indeed's data and insights to deliver useful tips to help guide your career journey.

Before you make a financial decision, you can learn the unique elements of finance, including definitions and formulas. One of the most critical aspects of finance is simple interest and compound interest. Learning about both can help you make a more informed decision regarding savings, loans and investments. In this article, we explain simple interest vs compound interest, explore how to both with formulas and examples, describe the differences between each and explore use cases.

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## What is simple interest vs. compound interest?

To understand what is simple interest vs compound interest, you can learn the definition of interest. Interest is the cost or savings you can incur from a loan or investment. You can calculate simple interest by expressing it as a percentage of the initial borrowed amount. You can calculate compound interest based on the initial borrowed amount plus the interest accumulated over a certain period. As the initial principal or borrowed amount earns interest over a certain period, you can add the interest and the principal value to get a new principal amount.

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## How to calculate simple vs. compound interest

Here are three steps to help you learn how to calculate simple interest and compound interest:

### 1. Learn the difference

Simple interest relies on a constant principal amount while compound interest may require that you constantly revise the principal amount based on the interest it earns. For instance in compound interest, you can calculate the interest that accumulates for the first year as a proportion of the principal amount. You may then add the interest to the principal amount and use that value to calculate interest for the second year.

### 2. Discover the simple interest formula

The simple interest formula is a fast and easy method that you can use to calculate interest on fixed amounts. The two main variables of the formula include the initial borrowed amount and the interest rate which may often be a percentage. Here's a formula to help you understand the simple interest formula:

I = P x R

Where:

• I represents the simple interest

• P is the principal or initial borrowed amount

• R is the interest rate which you may express as a decimal

You can use this formula to find the interest of a loan over a specified period:

I = P x R x T

Where T is the duration of the loan and you can express it in years.

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### 3. Explore the compound interest formula

To calculate compound interest, you can choose to use the simple interest formula or the compound interest formula depending on the period. For long periods you may use the compound interest formula while for short periods the simple interest formula may be more useful. Here's an outline of the compound interest formula:

I = P[(1 + R)n - 1]

Where:

• P is the initial borrowed or principal amount

• R is the interest rate

• n is the number of years

To calculate the interest more than once a year, you can use the following formula:

I = P[(1 + R/ M)nM - 1]

Where:

• P is the initial borrowed or principal amount

• R is the interest rate

• n is the number of compounding periods

• M is the number of times you may like to compound the interest every year

## Simple interest calculation examples

Here are some sample calculations to help you understand how to calculate simple interest:

### Example 1

Here's a calculation to help you learn how to calculate simple interest:

Yolanda's Gift shop borrowed £10,000 from a London bank to finance an expansion. The bank gave them an interest rate of 5% for the loan. Here's a breakdown of the interest they may pay:

Simple interest = Principal x Interest rate

Simple interest = £10,000 x 0.05

Simple interest = £500

This means that Yolanda's gift shop may pay an additional £500, leading to a total payment of £10,500.

### Example 2

Here's a simple calculation to help you understand how to use the simple interest formula:

John's Pizza Place invested in stocks worth £2,000. The stock company set interest they can earn at 12% for four years. Here are calculations to show the total interest they earned:

Simple interest = Principal x Interest rate x Time

Simple interest = £2,000 x 0.12 x 4

Simple interest = £960

This means that at the end of the four years, they can receive £2,960.

## Compound interest calculations

Here are examples of calculations that can help you understand how to calculate compound interest:

### Example 1

Here's an example of how to calculate compound interest using the simple interest formula:

Jennifer opened a savings account with her local bank and deposited £2,000. The bank allowed her to have a compound interest rate of 2.8% for two years. Here are the calculations for the compound interest her savings account helped her earn:

You may first calculate the interest for the first year:

Interest = Principal x Interest rate

Interest = £2,000 x 0.028

Interest = £56

This can mean at the end of the first year, they earned £56, so the new principal amount at the beginning of the second year is £2,056.

You can then calculate the extra interest for the second year using the simple interest formula again:

Interest = Principal x Interest rate

Interest = £2,056 x 0.028

Interest = £57.57

You can then add the two separate interests to the initial deposit amount to get the total money in the savings account by the end of the second year. Here's the final breakdown:

Total interest = £57.57 + £56

Total interest = £113.57

Total amount in the savings account = £113.57 + £2,000 = £2,113.57

### Example 2

Here's an example of how to use the compound interest formula in a calculation:

A student's organisation can issue student loans worth £10,000 with a compound interest rate of 5% that they compound every year. They can allow students to repay the loan over the next three years. Here's an outline of the calculations for the loan's compound interest:

Interest = Principal [(1 + interest rate) number of years - 1]

Interest = £10,000 [(1 + 0.05)3 - 1]

Interest = £10,000 x 1.57625 - 1

Interest = £1,576. 25

This can mean that the organisation requires the students to repay £11,576.25 at the end of the three years.

### Example 3

Here's a calculation that can help you understand how to use the compound interest formula:

Julia invested in stocks with an interest rate of 10% every month for two years. They invested £6,000. Since they may choose to compound the interest every month, this can mean that the number of compounding periods is 12. Here's an outline of the compound interest her investment earned:

Interest = Principal [(1 + interest rate/ number of compounding periods annually) number of years x number of compounding periods - Principal]

Interest = £6,000 [(1 + 10/12)2 x 12 - £6,000]

Interest = £7,322.35 - £6,000

Interest = £1,322.35

This means that after two years, Julia had £7,322.35.

## Concepts that apply the compound interest principle

Numerous concepts in finance may use the compound interest formula or concept. Here are two fundamental values that you can closely associate with compound interest:

### Time value of money (TVM)

This value may rely on the concept that a sum of money in the present time can be worth more than the same sum in the future because of current earning potentials. Earning potential can reflect the most significant potential profit you can get from a sum of money. You can calculate the time value of money using the same concept as compound interest. This is because it can assume that every year the value of a sum of money can increase or decrease based on factors such as investments and inflation.

The concept can help investors decide between two projects. For instance, between an investment that can promise a £6,000,000 payout after one year and one that may promise the same after three years, the former can be a better option. This is because £6,000,000 after one year has a higher present value than it may ever have after three years. Here is the formula you can use to calculate the time value of money:

FV = PV * [1 + (i/n) ] n * t

Where:

• FV is the future value of money

• PV is the present value of money

• i is the interest or growth rate

• n is the number of compounding periods annually

• t is the number of years

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### Rule of 72

You may use the Rule of 72 to calculate how long it can take for an investment project to double in value time based on an annual rate of return. It can be a helpful formula since it's easy and quick for you to use. You may also apply the concept behind the Rule of 72 to compound interest calculations that have an interest rate between 6% and 10%. Here's a formula you can use:

Y = 72 / R

Where Y represents the years an investment may take to double in value and R is the interest rate.