What is Compound Interest?
Compound interest is the interest on money you deposit initially. With the interest rate given, you earn accumulated interest over time. This is one of the best savings strategy where your money grows passively.
How to use the Simple Compound Interest Calculator?
- Enter the initial Start Amount;
- Enter the Annual Interest Rate provided by the institution;
- Enter the Compound Frequency (ask the institution about interest rate compounding frequency);
- Enter Years of Growth (years you plan to keep the savings compounding);
- Enter Contribution Amount (if you plan to deposit contribution and how much or leave blank);
- Enter your Contribution Frequency (If you entered an amount in step 5, how frequent will you contribute into the account?, otherwise leave blank if not contributing)
Scenario of Compound Interest after 5 years with monthly contribution.
You are investing $5,000 upfront, and you are also contributing an additional $100 every month for the next 5 years. The money grows at an annual interest rate of 6%, and the interest is compounded monthly, meaning it’s added to the total balance every month, making the investment grow even faster.
How it works:
Initial Investment: You start with $5,000.
Monthly Contributions: Every month, you add $100. Over 5 years, that’s a total of $100 x 12 months x 5 years = $6,000 in contributions.
Interest Growth: The interest is applied to both the initial investment and your monthly contributions. Every month, the interest is calculated on the growing total amount of money. Over time, as your contributions and the interest itself grow, the balance increases more quickly.
Total at the End: After 5 years, the combination of your $5,000 starting amount, the $6,000 in monthly contributions, and the interest added over the 60 months results in a final balance of about $13,639.71. This includes both the principal (your original investment and monthly contributions) as well as the interest earned.
Interest Earned: The interest earned, in this case, would be about $2,639.71. This is the extra money you made from the compounding interest over the 5-year period.
So, at the end of 5 years, your investment will grow to about $13,639.71, of which $2,639.71 comes from the interest.
Is Compound Interest in Savings Similar to Investment?
Compound interest and investment are related concepts, but they are not the same thing.
Compound Interest:
Compound interest refers to the way interest is calculated and added to an investment or loan. It’s “interest on interest.” Instead of just earning interest on the initial amount of money (the principal), you also earn interest on the interest that has already been added to your account.
How it works: Every period (usually monthly, quarterly, or yearly), the interest you earned gets added to the principal. This new total is then used to calculate the next round of interest, so your investment grows faster over time.
Example: If you start with $1,000 and get 5% interest compounded yearly, after 1 year, you’ll earn $50 (5% of $1,000). In the second year, you’ll earn interest on $1,050 (your initial $1,000 plus the $50 interest from the first year), so you’ll earn more interest in the second year.
Investment:
An investment is the act of putting money into something (like stocks, bonds, real estate, or savings accounts) with the expectation of earning a return. The goal is to grow your money over time, often through interest, dividends, or capital gains.
How it works: You place your money in an investment, and over time, it may increase in value because of interest, market growth, or profits generated by the investment. The amount of return you earn depends on the type of investment and its performance.
Example: If you invest in a savings account with compound interest, your investment grows over time because of the interest. Or, if you buy stocks, your investment grows if the stock price increases.
The Connection:
Compound interest is one way that an investment can grow. In fact, many savings accounts and investments, like certificates of deposit (CDs or FDs) or bonds, use compound interest to help your money grow.
Investment, on the other hand, is the broader action of putting your money somewhere with the goal of making it grow, which could involve earning interest (compound or simple), dividends, or the value of the asset itself increasing over time.
In Summary:
Compound interest is a method of earning interest on both the initial amount of money and the interest that has already been added.
Investment is the overall process of placing your money into something to generate returns (like compound interest).
In short: Compound interest is a tool that helps your investment grow faster! It’s not an investment itself, but it’s often a key part of how investments grow.
Let’s take a look at the differences between How to Calculate Simple Interest, and How to Calculate Compounding Interest with Formulas.
What is Simple Interest?
Simple interest is basically the extra money you make on an investment (or owe on a loan) based on the original amount (called the principal). It’s like getting a “thank you” bonus for letting your money sit somewhere for a while.
How to Calculate Simple Interest? Formula for Simple Interest:
Simple Interest (SI)=Principal (P)×Rate (R)×Time (T)\text{Simple Interest (SI)} = \text{Principal (P)} \times \text{Rate (R)} \times \text{Time (T)}
Where:
Principal (P) is the original amount of money you invest or borrow.
Rate (R) is the interest rate (usually in percentage form).
Time (T) is how long the money is invested or borrowed, usually in years.
Let’s break it down with an example:
Imagine you invested $1000 in a savings account with an interest rate of 5% per year for 3 years.
Principal (P) = $1000
Rate (R) = 5% = 0.05 (we convert percentage to decimal by dividing by 100)
Time (T) = 3 years
Now plug those numbers into the formula:
SI=1000×0.05×3\text{SI} = 1000 \times 0.05 \times 3 SI=150\text{SI} = 150
So, in 3 years, you would earn $150 in interest.
Total Amount (A) after interest:
To find out how much you have in total after 3 years (principal + interest), you just add the interest to the principal.
Total Amount (A)=Principal (P)+Simple Interest (SI)\text{Total Amount (A)} = \text{Principal (P)} + \text{Simple Interest (SI)} A=1000+150=1150\text{A} = 1000 + 150 = 1150
So after 3 years, you’d have $1150 in total.
Key Points to Remember:
Simple interest is always calculated on the original principal amount, not the interest that accumulates each year.
The formula is pretty straightforward: Principal × Rate × Time.
The longer you keep the money invested or borrowed, the more interest you’ll make or owe.
A Quick Tip on How to Calculate Simple Interest:
If you ever forget the formula, think of it like a “3-step dance”:
Principal (P) = How much you start with.
Rate (R) = How much it grows each year.
Time (T) = How long you’re letting it grow.
What is Compound Interest?
Unlike simple interest, which only earns interest on the original amount of money (the principal), compound interest earns interest on both the principal and any interest that has already been added to it. So, it’s like your money is working for you, and as time goes on, it earns interest on top of interest. This is often called “interest on interest.”
The more often interest is compounded (monthly, quarterly, etc.), the faster your money grows. It’s kind of like getting a snowball that rolls downhill and gets bigger and bigger.
How to Calculate Compound Interest? The Formula for Compound Interest:
The formula for compound interest looks a little more complicated, but don’t worry, it’s not bad once you break it down:
A=P(1+rn)ntA = P \left(1 + \frac{r}{n}\right)^{nt}
Where:
A = The amount of money accumulated after interest (the total amount, including the principal and the interest).
P = The principal (the initial amount of money you invested or borrowed).
r = The annual interest rate (expressed as a decimal).
n = The number of times the interest is compounded per year. For example:
Annually = 1
Quarterly = 4
Monthly = 12
Daily = 365
t = The time the money is invested or borrowed for, in years.
Let’s Walk Through an Example:
Imagine you invest $1000 at an annual interest rate of 5% for 3 years, and the interest is compounded quarterly.
Principal (P) = $1000
Annual Interest Rate (r) = 5% = 0.05 (convert to decimal)
Compounding Frequency (n) = Quarterly = 4 times per year
Time (t) = 3 years
Now, let’s plug everything into the formula:
A=1000(1+0.054)4×3A = 1000 \left(1 + \frac{0.05}{4}\right)^{4 \times 3}
Step 1: Break it down inside the parentheses
First, calculate the interest rate per compounding period:
0.054=0.0125\frac{0.05}{4} = 0.0125
Now, add 1 to this value:
1+0.0125=1.01251 + 0.0125 = 1.0125
Step 2: Exponent (raising to the power of 4×3=124 \times 3 = 12 compounding periods)
Now, calculate the exponent part:
1.012512≈1.16161.0125^{12} \approx 1.1616
Step 3: Multiply by the principal
Now multiply that by the principal $1000:
A=1000×1.1616=1161.60A = 1000 \times 1.1616 = 1161.60
Final Answer:
After 3 years, with quarterly compounding at a 5% interest rate, your total amount (principal + interest) will be $1161.60.
The Extra Interest Earned:
To find out how much interest you earned, subtract the original principal ($1000) from the total amount ($1161.60):
1161.60−1000=161.601161.60 – 1000 = 161.60
So, you earned $161.60 in compound interest over 3 years!
A Quick Summary of How to Calculate Compound Interest:
Compound interest means you earn interest on both your original amount and any interest that’s been added.
The formula: A=P(1+rn)ntA = P \left(1 + \frac{r}{n}\right)^{nt}
The more frequently the interest is compounded, the more you’ll earn (monthly, daily, etc.).
Compound interest grows faster over time than simple interest, especially with a long time horizon.
Real-World Example:
Think of compound interest like this: you plant a seed (your principal), and as it grows (time passes), it spreads roots (interest), and each new branch grows even more leaves (interest on the interest). Over time, it gets bigger and bigger—way faster than just a regular plant!
