Albert Einstein is credited with the famous financial saying: “Compound interest is the eighth wonder of the world. He who understands it, earns it ... he who doesn't ... pays it.” And he was right. Compound interest is magical.

People invest to make money. Most of them do that in the hopes of letting compound interest work on their original investment over time. And most times, it does. When compound interest works positively, you can build a significant amount of wealth so long as you leave your original investment alone for a while.

But the reverse is also true. If you have a loan that attracts compound interest, it can render you bankrupt given enough time. That’s because it will build up and spiral out of control.

Therefore, it helps to learn how compound interest works and the formula for maturity value of compound interest. The latter can help you determine how much wealth or debt you will end up with after a specified period.

## Calculating Compound Interest

Before you tackle the formula for maturity value of compound interest, it would be best to learn the common terms people use during such calculations.

### 1. Considering the Principal

The principal is the original amount of money that you invest or borrow, and is the base number upon which the interest is calculated and thus determines what your final value is.

When calculating compound interest, the principal often changes. At the beginning of each period, the principal becomes the original sum plus the interest it earns over the previous period. But for simple interest calculations, the original amount remains constant.

### 2. Knowing the Interest Rate

Interest rate is the amount charged by lenders to borrowers when they get credit. But it also refers to the amount you receive within a specified period compared to the principal when you invest your money.

It is usually expressed as a percentage and is mostly calculated on a yearly basis. However, some interest rates may apply two or more times each year.

For simple interest, the rate only applies to the first original amount you invested. But for compound interest, the interest rate applies to the principal and the interest it accumulates the previous year. And that is where the magic of compounding happens because it magnifies the principal over time.

### 3. Considering the Compounding Period

The compounding period refers to when a specified interest rate applies when doing calculations. It is the time between when your principal was compounded in the past and the next time it will be compounded again.

Typically, compounding periods are usually one year long. But they can be less or more than that, which means they can be as short as a few days or as long as a decade. So, you may end up with fractions or multiples of the base compounding periods.

Generally, the more times you compound the principal within a pre-determined period, the more money you end up with.

### 4. Knowing the Periodic Rate

Periodic rates refer to the rates over a period that is separate from what the interest rate is based on. And they may result in fractions or multiples of the set interest rate.

If compound interest applies several times a year, it is known as intra-year compounding. And when it occurs, it means you must divide the annual interest rate by the number of compounding periods within that year. For example, if the annual interest rate is 10 percent and compounding occurs quarterly, the periodic rate is 10/4, resulting in 2.5 percent.

### 5. Understanding the Maturity Value

The maturity value refers to the total amount due to you on the due date of your investment, usually after the compounding period is complete. It includes both the principal and all the interest it has accrued. And it varies for simple and compound interest.

## Formula for Maturity Value of Compound Interest

The maturity value formula for compound interest can be obtained by multiplying the principal by one and adding the interest rate raised to the number of total compounding periods.

A=P (1+r/n) ^{nt}

Where A = Maturity Value

P = Principal

r = Interest rate per year

n = Number of times the interest is compounded annually (compounding frequency)

t = Total compounding period in years

### Example 1

What is the future value of $10,000 on deposit for 5 years at 6 percent simple interest?

**Answer 1**

For simple interest, the maturity value A = P (1+rt)

So, in this case, the future value of $10,000 would be: 10,000(1+6/100*5) =$13,000

### Example 2

What is the future value of $10,000 on deposit for 5 years at 6 percent annual compound interest?

**Answer 2**

For compound interest, the maturity value A=P (1+r/n) ^{nt}

In this case, A = 10,000(1+0.06/1)^{5}, which equals $10,000(1.06)^{5}

Therefore, based on the formula for maturity value of compound interest, in this example, A = $13,382.

### Example 3

What is the future value of $10,000 on deposit for 5 years compounded quarterly at a rate of 6 percent per annum?

**Answer 3**

Based on the formula A=P (1+r/n) ^{nt}

Where n = 4 and t = 5,

A= 10,000(1+0.06/4)^{20}

In this case, A = 10,000(1.3468), which equals $13,468.55

There is clearly a difference between compound and simple interest. Also, you can see that the more times compounding occurs, the more money you will make over time. So, please invest now and let time work in your favor. And if you have debts, it would be wise to begin paying them down as soon as possible before they become unmanageable.

References

- Quotes on Finance: Albert Einstein - Compound interest
- Corporate Finance Institute: What is an Interest Rate
- AccountingTools: Compounding period definition
- Boe.Ca.Gov: Time Value of Money - Six Functions of a Dollar
- Bankrate: What is the principal?
- EduCBA: Maturity Value Formula
- Cuemath: Compound Interest

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