What is Compounding Interest?

Compounding interest is a simple, yet powerful concept that can have a positive effect on your savings and investments but a negative effect on your loans. The Balance defines compound interest as “interest earned on money that was previously earned as interest.” It all starts with the concept of simple interest and involves some key factors such as the principal amount, the annual interest rate, the time factor and the compound period.

Calculating Simple Interest

To calculate compounding interest, you must first begin with the formula for simple interest. Simple interest is an easy method used to calculate interest charges on loans. It multiplies the principle by the daily interest rate by the

Simple Interest Formula

Simple interest = P x i x n

Where P = principle, i = interest rate and n = loan term

Let’s say that you have a $25,000 car loan from the bank, payable over a period of 5 years, with an interest rate of 7%. Using the simple interest formula P x i x n, you can calculate how much interest is payable over the duration of the loan.

P = 25,000 , i = 0.07 , n = 5

Therefore, the interest payable on this loan over the 5 year loan term is:

25,000 x 0.07 x 5 = $8,750.00

This means that you are paying 1,750 in interest each year or approximately 145.83 each month. You will owe a total of $33,750 to the bank.

Similarly, for savings, the simple interest formula can be used to calculate how much interest you will earn on your deposit. Let’s assume that over the course of one year you deposited $600 and the bank pays 2% interest. At the end of the year, the interest earned would be:

600.00 x 0.02 x 1 = $12

So, your balance at the end of the year (ignoring bank fees) would be $612.

To calculate your earnings, for the next year, compounding interest will come into play.

Simple Interest Calculators

Here are a few simple interest calculators that you can use:

Simple Interest Calculator (Web Math)
Simple Interest Calculator (Money Chimp)

Calculating Compounding Interest

In year one, using the simple interest formula on your savings, you earned $12 in interest, which turned your $600 into $612. With compounding interest, you will be earning on your principal plus any interest earned. The formula for compounding interest is:

A = P ( 1 + r/n) ˄ (nt)

Where,

A is the amount after a certain amount of time
P is the initial amount you started with
r is the annual interest rate
n is the number of times that the interest is compounded
t is the number of years in the term

Using an initial deposit of $600, this what your savings could look like (ignoring pesky bank fees) after ten years, using the compounding interest method:

P = 600 , R = 0.02 , N = 12 , T = 10

Using the formula: A = P ( 1 + r/n) ˄ (nt)
Insert the numbers above into equation: A = 600 (1 + (0.02 / 12) ) ˄ (12 x 10)
A = 600 (1.0017) ˄ 120
A = 600 (1.22609)
So, A = 735.65

At the end of 10 years, you would have earned approximately $135.65 in interest.

Conversely, for the $25,000 car loan from the bank, payable over a period of 5 years, with an interest rate of 7%, you would actually be paying back $35,063.79 in total:

Insert the numbers above into equation: A = 25,000 (1 + (0.07/1)) ˄ (1 x 5)
A = 25,000 (1.07) ˄ 5
A = 25,000 (1.4026)
So, A = 35,063.79

Please note that there are various types of compounding schedules that are used to calculate interest. Interest can compound yearly, monthly or daily or on any other schedule. In the example above it is compounded once per year. Be mindful that these various schedules can result in varying results.

If you want to calculate the compounding interest over one year, Investopedia provides two additional formulas::

Compound interest = [P (1+i) ˄ n] − P

Compound interest = P [(1+i) ˄ n − 1]

Where:

P = Principle
i = interest rate in percentage terms
n = number of compounding periods for a year

Compound Interest Calculators

Compound calculators make it very easy to see the changes in earnings or spending due to the compounding schedule. Here are a few compound interest calculators that you can use for quick calculations:

How to Use Compounding Interest to Your Benefit

There are several ways that you can use compound interest to your benefit. This is even possible with loans, where banks usually benefit from the accrued interest that you pay.

Pay more than the minimum on credit cards
Pay extra towards your other debt
Consolidate debts if you can get a lower interest rate
Start saving as early as possible
Use different methods to save money
Review your bank’s compounding interest schedule
Keep adding money to your savings/investment pot
Make saving or investing a long-term activity
Reinvest earnings wherever possible
Keep an eye on fees charged on accounts