When it comes to finance, it is good that one should understand what is compound interest, and also how to calculate it.
Many investors that invest into the financial market doesn’t really know what compound interest is all about.
You need not to worry as i have given you a detailed article on what it is
If you have been investing in the financial market like the mutual funds, fixed deposit, or even the treasury bills (secondary market), in one way or another you might have come across the term compound interest.
Is quite unfortunate that some of our financial institutions will not give in details or explain to their customers what the term is.
What is compound interest
Compound Interest definition: This is an interest earned on previous interest in an investment.
You can say that it an interest on an investment’s interest, plus previous interest.
Many a time we invest in any financial markets like stocks, fixed deposit, mutual funds, at maturity we tends to collect both the interest accrued and the principal.
With this, you can’t have a compound interest.
It only comes up if you leave the interest accrued on maturity, and continues to do that depending on the number of months you’re investing.
For example, if you earn a 5% annual interest on mutual funds, a deposit of one million naira would gain you fifty thousand naira after a year.
Then the question is what happens the following year?
This is actually where the compounding now comes in.
You’ll earn interest on your initial deposit, and you’ll earn interest on the interest you just earned.
If you deposited the sum of N200k, with an interest rate of 5%, at maturity you receives an interest of N15k.
The N15k interest will also generate another interest rate of 5% even if you didn’t deposit any money to your account.
Let me use the fixed deposit account for another example.
You invested N500k to your fixed deposit, with an interest rate of 7% for six months.
Let’s assume that at maturity you will earn N100k
At the end of the investment, bank will you N100k, plus the money you invested making it a sum total of N600k.
However, if you leave the interest which is N100k, and reinvest the N500k again, the previous interest rate which is N100k will get another interest for you.
But to be on a safer side especially here in Nigeria, you need to find from your bank on how often interest is being compounded on your fixed deposit investment or any other investment.
Compound interest isn’t applicable to only when you’re investing or savings money in the bank, if you’re borrowing money from any financial institution, it works a well and this time against you.
For example you borrowed the sum of one million naira from the bank, and let’s assume that the interest is N70k.
When at due date and you pay, the interest which amounts to the money you borrowed will begot another interest on top and this continues till you pay up.
But before going into taking of loans from any financial institution, you must first inquire if they will include compound interest on it.
Generally, compound occurs when interest gets added to the principal amount invested or borrowed, and then the interest rate applies to the new principal.
In terms of investment and savings, compounding works best for you, as it helps to grow your savings and investment.
On the other hand, it works against you in the case of borrowing money from your bank or any other financial institution.
How Compounded Interest Works
Let me further explain how compound interest works, especially in the layman’s way.
Let’s say you invested N1,000 into a treasury bills or mutual fund account with a 10% interest rate that compounds annually.
At the end of the first year, you’ll have N1,100 with the initial N1,000 in principal plus N100 in interest.
The N100 is the simple interest, the interest based only on the principal amount invested.
Then at the end of the second year, you’ll have N1,210, and N1,100 from the previous year, plus N110 in added interest.
That is 10% of N1,100 which gives you N110 respectively.
Then instead of you calculating the interest based only on your original principal, compounding interest calculates your annual interest based on the principal plus any previous interest you earned on that principal.
So the compound interest doubles your interest as years goes by, as long as you kept the money in your account, without withdrawing it.
Please note that immediately you make a cash withdrawal from the interest accrued, everything comes to end.
So the more you leave the money in your account, the more your interest doubles.
Compound Interest Formula
Before going into the calculation, you need to first know the compound interest formula.
You can’t calculate your compounding without having the formula.
The formula to calculate compound interest is:
A = P (1 + r / n) ^ nt
Let me explain what those letters means:
- A: Means the amount you will end up with
- P: This means the principal, that is the money you deposited into your account or invested with
- r: the annual interest rate, written in decimal format
- n: This is the number of compounding periods per year
- t: This is the amount of time usually in years that your money compounds. In investment, it can also be in months.
So the above is compound interest formula, with which you will use for your calculations.
How to calculate compound interest
Having giving you the formula, next is how to calculate compound interest.
It isn’t a difficult one, as long as you have the formula with you.
However, to make things easy for you, you can choose to use any of the online calculations as they are accurate and really helpful.
Compound interest examples:
Let’s say you invested N50,000 into your savings account, with annual compounded interest rate of 5% for 10 years.
The calculation will be as follows;
P is 50,000
r is 0.05 that is percentage of 5 is 0.05
n is 12, that is one year
t is 10, which is how long the interest will be compounded
Using the compound interest formula A = P (1 + r / n) nt the calculation is
A = 50000 ( 1 + 0.05 / 12) ^ ( 12 × 10)
A = 50000 (1.00417) ^ (120)
A = 50000 (1.64767)
A = 50000 × 1.64767 = 82383.5
To elaborate more on the calculation, i added 1 + 0.05 and divided it by 12, which gives me 1.00417.
If you multiply 12 by 10, it gives you 120.
To get the 1.64767, you will say 1.00417 to the power of (^) 120 which gives you 1.64767.
To get make it easier for you, download any exponent calculator on play store, or you can use your scientific calculator as well.
So after ten years, you will have a compound interest of N82,384 if you decided to round it up.
As long as you have the formula with you, calculating compound interest isn’t a difficult one at all.
Another easy way to calculate a compounded interest is through excel. It helps a lot especially if you know how to use it.
Note the formula is different when using excel for your calculation.
The formula is FV (rate,nper,pmt,pv)
I’m not that good in excel, so i didn’t bother to know about calculation on spread sheet using excel.
When you look at compound interest, you’ll see that it will help to double one’s investment or savings, but the truth is that not many financial institutions especially in this country accepts or make use of it.
However, when giving out loan to you, the will tell you that the interest accrued is compounded.
Difference between compound and simple interest
Two terms might seem similar, but actually they are different.
Simple Interest is the percentage interest one gets from the principal.
The formula to calculate the simple interest is = P × r × n
where:
P=Principal amount
r=Annual interest rate
n=Term of loan, in years
For example you made an invest of N200k for one year, which gives you an interest of N10k per month.
That monthly interest is the simple interest, while the interest accrued on the monthly interest of the principal is the compound interest.
This is the difference between compound and simple interest.
Interest are usually compounded in
- Daily
- Weekly
- Monthly
- Quarterly
- Annually
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This is where i wrap it up on compound interest formula and the calculation involved.