Compound Interest
In this topic, you will learn the concept of compound interest and how it is used to model real-world financial situations.
Compound interest is calculated not only on the original amount (principal) but also on the interest that has been previously added. This means the amount grows over time at an increasing rate. You will become familiar with key terms such as principal, interest rate, time, and compounding periods.
Related Lessons:
What Is Compound Interest
In this video, we are going to learn what is the difference between simple interest and compound interest.
We will learn that the difference between simple and compound interest is the action that we take at the end of each calculation, whether to withdraw or add the interest to the principle.
Compound Interest Formula
The compound interest formula is:
\(Total=P(1+\frac{𝑟}{100})^𝑛\)
where:
- Total is principle plus the interest
- P is the principle amount
- r is the interest to compound
- n is the number of times to compound
Compound Different Duration
In this topic, you will learn how different compounding durations affect the growth of compound interest. The duration refers to how often the interest is calculated and added to the principal, such as half-yearly, quarterly, or monthly. Using the same compound interest formula, we will adjust the variables accordingly.
Compound half year
We divide the interest rate by 2, and multiply the duration by 2 since one year there is two half year in one year.
\(Total=P\left(1+\frac{\left(\frac{R}{2}\right)}{100}\right)^{2\times n}\)
Compound quarterly
We divide the interest rate by 4, and multiply the duration by 4 since one year there are four quarters in one year.
\(Total=P\left(1+\frac{\left(\frac{R}{4}\right)}{100}\right)^{4\times n}\)
Compound monthly
We divide the interest rate by 12, and multiply the duration by 12 since one year there are 12 months.
\(Total=P\left(1+\frac{\left(\frac{R}{12}\right)}{100}\right)^{12\times n}\)
Example 1
Sandy invests $15000 at an annual rate of 4% compound interest. If she withdraws all the money after 5 years, how much will she receive?
Example 2
Susan invests $29 480 in a bank that pays compound interest at a rate of 3.96 % per year, compounded half yearly. Find the amount that Susan has in the bank after 3 years, leaving your answer to the nearest cent.