Increase is an exciting word to most people. But compound interest is a special kind of increase that has been described as magic.
Compound interest works by adding earned interest to the original amount (principal) so that both the principal and interest earn interest.
To achieve this, each time interest is earned it should be reinvested and not withdrawn.
However, compound interest also has a dark side—if you owe money. Your unpaid loan can quickly build up because any outstanding amount you owe gets added to the original loan and also attracts charges.
The Variables of Compound Interest
To understand compound interest, you need to know the 5 essential variables that go into calculating it:
- Interest Rate: This is the rate at which the money earns or is being charged. The higher this rate is, the higher the interest generated
- Principal Amount: This is the amount you start with. The higher it is, the more interest you can earn or get charged.
- How Often To Compound: How frequently is your money compounded? Is it yearly, monthly, daily, or even continuously? The more frequently your money is compounded, the faster or higher it earns.
- Period or Duration: The longer your money is allowed to be in the account, the more it grows.
- Deposits and Withdrawals: Over the life of the investment, one has the option to make new deposits or withdrawals. Deposits increase the interest earned while withdrawals reduce it
Compound Interest vs Simple Interest
If you borrow $3,000 to be repaid after 3 years, compound interest works out the following way.
Year 1: 3,000 x 8/100 = 240
Year 2: 3,240 x 8/100= 259.2
Year 3: 3,499.2 x 8/100 =279.936
Amount after 3 years:
3,000 +240 +259.2+279.936 = 3,779.136
This can be contrasted with a simple interest in which there is no compounding. The same sum of money will give you:
Year 1:3000 x 8/100 =240
Year 2:3000 x 8/100 =240
Year 3:3000 x 8/100 =240
Total amount: 3000 +(3 x 240) =3,720
For simple interest, the interest amount earned each year is the same (240) but for compound interest, it increases with each year. (240, 259.2, 279.936)
Compared with simple interest, compound interest earns you more money.
This unique feature of compound interest highlights an important fact about time and money: if you save sooner, you reap rewards. If not, you will need to save harder to catch up on lost time.
The Compound Interest Formula
The formula for compound interest has four parts.
- P: your initial amount or principal
- r: rate of interest
- n=number of periods
- A: the total amount you get at the end of the periods
The formula for compound interest is A=P(1+r)^n
This formula makes it convenient to get the total amount in one step without repeating the calculation for each year.
Here are 10 examples of compound interest in real life
1. Loans
Compound interest is used in financial products such as mortgages, personal loans, or student loans.
For example, if you owe a $5,000 student loan that accrues at 7% (0.07), at the end of 5 years, you will owe: A= P(1+r)^5= 5,000 (1+0.07)^5=$206,575
2. Credit cards
Credit cards are a popular method for making purchases. They can also incur huge fees due to outstanding debt that ends up being compounded.
3. Bank accounts
This can be either savings accounts or Certificates of Deposit (CDs)) which can earn holders attractive returns.
In most cases, the money cannot be accessed for long periods. In exchange for this, the bank offers higher interest which is usually compounded monthly.
4. Population Growth and decay (reduction)
You can estimate future population numbers using compound interest. For example, if a city has 30,000 people and its population grows at 10% per year, in 4 years’ time it will be:
Initial population, P = 30,000
Growth rate, r = 10% = 0.1
Period n = 4 years
Calculation: A =P (1 + r) ^n = 30,000 (1+0.10) ^4= 43,923
5. Compound Inflation Protection
Health care inflation insurance helps to protect against unexpected rises in prices in nursing costs for people in old age.
When purchasing insurance to cater to their old age, people are advised to consider products with compound inflation.
Compound inflation is considered better than simple inflation because it gives more benefits and security.
6. Bacteria multiplication
Bacteria multiply fast through the laws of compound interest.
For example, if bacteria of 80,000 breed at a rate of 2% after every hour, how many will they be after 24 hours?
Initial amount P NM= 80,000
Rate r = 2% = 0.02
Periods= 24
Calculate 80,000 (1+0.02) ^24=128,675
7. Compound Depreciation of assets
Compound interest (depreciation or decay) can be used to estimate the value and useful life of a machine.
For example, if a piece of equipment costs $10,000 and its depreciation rate is 2% (0.02), after 3 years its value is:
A=P(1+r) ^n
10,000(1+ [-0.02]) ^3= is $9,411.92
(We use – 0.02 instead of 0.02 because this is decay or depreciation rate, not an increasing rate)
8. Pension payments
For companies to pay pensions to their employers, they contribute some amounts into investment accounts.
After these have accumulated over the years, they become available to support retirees.
This process is aided by compound interest which gives better returns and guaranteed
income.
9. Generating Profits For Companies
Compound interest is a source of profits for companies. e.g., for financial managers to provide dividends for their investors, they accumulate and compound them by reinvesting.
This will lead to higher dividend payouts to investors
10. Multidisciplinary nature of compounding
Compounding principles can be extended to other life areas such as relationships, or learning.
Compounding is based on the long-term instead of immediate gratification.
In many activities, people who base their goals on the long term tend to succeed better than those with a short-term focus.
Conclusion
Compound interest drives many aspects of our lives. As you can see, it can be applied in many areas such as finance, economics, science, and more.