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# Compound Interest Explained: Definition, Formula, Real Examples

### What is Compound Interest?

Compound interest is the interest on a deposit or loan that is calculated not only on the initial principal but also on the accrued interest from prior periods. Compound interest is also known as interest on interest because the borrower has to pay interest on principal as well on previous interest. Of course, it provides a greater return on investment than simple interest, which is calculated exclusively on the initial principal.

### How To Calculate Compound Interest: Formula Explained

Learning how to calculate compound interest is not difficult when you understand the compound interest formula, that is:

FV = PA*(1+i/n)nt

Let's break down the individual components of the compound interest formula:

• FV is the future value of the investment, including interest.
• PA stands for principal amount and is the initial investment amount on which is calculated the first interest payment.
• i stands for interest rate and is the rate that is paid on the sum of the principal amount plus any previous interest paid.
• n is the compounding frequency, which is the number of times the interest compounds yearly. In other words, the compounding frequency defines how many times a year the borrower must pay interest. Usually, it is monthly, quarterly, or annually.
• t is the investment time horizon, which is the number of years the principal amount is borrowed or invested.

### Compound Interest Example Calculation

To illustrate, we can conduct a compound interest example calculation. Let’s assume Alex invests \$100,000 in a high-yield saving account with an interest rate of 3%, compounded quarterly. Alex could use the compounded interest formula to calculate the investment's future value after twenty (20) years:

FV = \$100,000*(1+0.03/4)20*4

The future value of Alex's investment after twenty (20) years would be \$181,804. To determine the exact amount earned with compound interest, we should subtract the deposit's principal from the calculation. Here's the formula for calculating compound interest earnings alone:

CI = PA*(1+i/n)nt - PA

### The importance of the compounding frequency

It is worth noting that the higher the compounding frequency, the higher the investment’s return. That happens because compound interest is calculated both on the principal amount and on the accrued interest from prior periods. To illustrate, let's calculate Alex's investment’s future value with an interest rate compounded quarterly instead of annually.

FV = \$100,000*(1+0.03)20

The future value of Alex's investment after twenty (20) years with a 3% interest rate compounded annually would be \$180,611, which is \$1,193 lower than the same amount invested at the same interest rate but with a quarterly compounding frequency.

### Simple Interest Vs. Compound Interest

Simple interest received or paid over an investment time horizon is a fixed payment calculated as a percentage of the borrowed or lent initial principal. On the other hand, compound interest is the interest on a deposit or loan that is calculated not only on the initial principal but also on the accrued interest from prior periods, giving the investor a greater return on their investment than simple interest.

To illustrate, let's calculate Alex's investment’s future value with a simple interest rate and compare the results with the same amount invested with a compound interest rate. Below is the formula to calculate the future value of an investment with a simple interest rate:

FV = PA*(1+i*t)

So, Alex's investment future value with a simple interest rate would be:

FV = \$100,000*(1+0.03*20)

The future value of Alex's investment after twenty (20) years with a 3% simple interest rate would be \$160,000, which is \$21,804 lower than the same amount invested at the same interest rate but with a quarterly compounding frequency.

### Manuel Bleve

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