Financial Modeling Tutorials

- Excel Modeling
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- Simple Interest vs Compound Interest
- Simple Interest Formula
- CAGR Formula (Compounded Annual Growth Rate)
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- Mortgage APR vs Interest Rate
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## What is Compound Interest?

The addition of the interest to the principal amount of the loan or the deposit, or rather say the interest on the interest is known as the Compound Interest. It is basically the outcome of reinvesting the interest and not paying it so that the interest is earned in the next period on the principal sum in addition to the formerly accumulated interest.

In simple terms, calculation of Compound interest is done on the amount borrowed and previous interest if any. It is very much standard in economics and finance. It is contrasted with the simple interest in which formerly accumulated interest is not included in the principal sum of the current period and hence, there is no such compounding here.

### Compound Interest Formula

Below is the formula for compounding interest calculation.

**A = P (1 + r/n)**

^{(nt)}Where,

- A = Future value of loan/investment, including the interest
- P = Principal investment amount i.e. the loan amount or the initial deposit
- r = Interest rate annually
- n = Number of times the interest is being compounded per unit
- t = Time period for which amount is borrowed or invested

### Example of Compound Interest Calculation

**In this example, X did the investment of $ 7,000 initially for a period of 3 years. Calculate the value of the investment after the period of 3 years when the investment gives the return of 10 % compounded monthly.**

**Solution:**

For the calculating value of the investment after the period of 3 years compound interest formula will be used:

4.9 (1,067 ratings)

**A = P (1 + r / n)**

^{nt}Given,

- A (Future value of the investment) is to be calculated
- P (Initial value of investment) = $ 7,000
- r (rate of return) = 10% compounded annually
- n (number of the times compounded annually) = 1
- t (number of years for which investment is done) = 3 years

Now, Calculation of Compound Interest will be –

- A = $ 7,000 (1 + 0.10 / 1)
^{1*3} - A = $ 7,000 (1 + 0.10)
^{3} - A = $ 5,000 (1.10)
^{3} - A = $ 7,000 * 1.331
**A = $ 9,317**

Thus it shows that the value of the initial investment of $ 7,000 after the period of 3 years will become $ 9,317 when the return is 10 % compounded annually.

### Types of Compound Interest

It usually consists of two types:

#### #1 – Periodic Compounding

In this method, the rate of interest is applied at regular intervals and then generated. This amount of interest is then added to the principal. Periods can be weekly, monthly, annually or half yearly.

#### #2 – Continuous Compounding

In this continuous compounding method, a formula based on the natural log is used that calculates the interest at the smallest possible time period. Here, the interest is included back to the principal. It can be leveled to a constant rate of growth for all natural growth. The figure was discovered from physics. This uses the Euler’s number that is the famous irrational number known to more than 1 trillion digits of accuracy. Letter “E” is used to denominate the Euler’s number.

### Pros

**Increase in Value of Investment Exponentially**– With the Compound interest, in the long run, the value of the investment increases exponentially. The interest is earned by the investor on principal as well as previously earned interest part of the investment so the investment in case of compound interest grow quickly depending on the rate of return and number of the compounding periods. It represents mainly the addition of the interest amount to the deposit.**Accumulation of Better Returns**– Mainly there are two types of interest that include simple and compound interest. The investment in case of compound interest accumulates better return when compared with the simple interest as in case of simple interest, interest is paid on the principal amount only that one has invested initially whereas in case of compound interest is paid on both principle amount and interest giving interest on previously earned interest as well.

### Cons

The main reason for the increase in the overall loan amount payment is because of the compound interest because one has to pay interest on principal as well as interest payment until and unless the whole of the money has been repaid. With the time if any interest amount remains unpaid, then the interest is to be paid on that remaining unpaid interest as well which created the vicious cycle for the borrower of the loan.

### Important Points

- While doing the calculation of compound interest, the number of the compounding period should be correctly used as it makes a significant difference. Generally when the compounding periods are more, then the compounding interest will also be more. So, before starting any calculation with respect to compound interest, compounding periods should be correctly taken into consideration.
- As the compounding is used in many areas including the loans, the borrower should know its annual payment rate exactly as the number of the compounding periods and the method of the calculation can have a serious impact on the monthly payments.
- It generally works in favor when the investment is considered while it works negatively from the borrowers perspective, but sometimes it works in favor of borrowers as well like instead of making the mortgage loan payment fully in a month, if the same is paid twice in a month, then it will cut down the amortization period thereby saving interest amount.

### Conclusion

One should have proper knowledge of the concept of the compound interest because it helps the person in making better financial decisions and saving a good amount of money. Compound interest formula is one of the very useful tools for the calculation of the future value of an investment, rate of investment, etc using the other available information. The interest under compound interest is earned by the investor on principal as well as previously earned interest part of the investment, so the investment in case of compound interest grow quickly depending on the rate of return and number of the compounding periods of the particular investment.

### Recommended Articles

This has been a guide to what is Compound Interest and its definition. Here we discuss compound interest formula and calculation along with practical examples. You can learn more about excel modeling from the following articles –

- Bond Premium
- Advantages of Premium Bond Amortization
- Exponential Distribution Definition
- Power of Compounding
- Monthly Compound Interest Calculation
- Daily Compound Interest Calculation
- Simple Interest vs Compound Interest
- CAGR Formula

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