Last updated on June 12th, 2025
Interest is the amount of borrowing money or the earnings on deposits. Simple interest is a method of calculating interest on an initial investment amount. For every time period, the interest rate remains constant. Whereas, compound interest is an approach to calculating the interest rate on both the principal amount and the interest earned previously. In this topic, we will explore simple interest and compound interest.
Simple interest (SI) remains unchanged over time, which is earned or paid on the original principal amount. This type of interest is used in loans such as student loans, installment loans, car loans, and so on. While the compound interest (C.I.) allows the money to increase faster over time.
This type of interest is used in investments and savings accounts. The interest rate of compound interest is higher than the interest rate of simple interest. Let us look at an example to understand this better. Suppose you deposit money in a bank and the interest rate is 2% per year. With simple interest, the money increases at a fixed rate. While with the compound interest, the investment amount grows faster beyond our expectations.
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The two main types of interest are simple interest (S.I) and the compound interest (C.I). Knowing the difference between the two types of interest and their formulas helps us make better financial decisions. The formulas of simple interest and compound interest are:
Simple interest = SI = P × R × T / 100
Compound interest = A = P (1 + R / 100n)nT
Now, let us understand the variables:
P = Initial amount
R = Rate of interest
T = Time duration
N = Number of times interest is compounded per year
Knowing these formulas will help increase earnings and minimize our debts by ensuring accurate calculations. By understanding the concepts of interest rates we can optimize our investments, manage the costs, evaluate the loan and repayment strategies.
To plan financial transactions, borrowings, and investments, we need to understand the properties and significance of simple interest and compound interest. Understanding the properties of both types of interest helps us make smarter financial decisions. It will help us to choose the best savings options and investing plans. The properties of simple interest are listed below:
The following is the list of properties of compound interest:
In our daily lives, we need to manage money more efficiently and plan for the future financial operations. Understanding the concepts of simple interest and compound interest is crucial for students to know how interest and money management work and to choose the right investment options.
Simple interest and compound interest have their own merits and demerits, making them vital in financial decision-making. Simple interest is best for short-term financial operations, while compound interest is more beneficial for long-term investments.
Advantages of simple interest:
Disadvantages of simple interest:
Advantages of Compound Interest:
Disadvantages of Compound Interest:
Simple interest and compound interest are the fundamental concepts in mathematics and finance. It teaches students how to manage money effectively by reducing future financial risks. However, mistakes in the calculation of simple interest and compound interest can lead to incorrect results and other problems. Here are some of the common errors and its helpful solutions to avoid them:
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Tom bought a house worth $50,000 and borrowed money from a bank at 5% simple interest per year for 10 years. Calculate the total amount he has to pay back after the period.
$75,000
To find the answer, we will use the simple interest formula, because the interest rate is fixed.
SI = P × R × T / 100
Here, P= $50,000
R = 5%
T = 10 years
Let us substitute the values:
SI = 50,000 × 5 × 10 / 100
50,000 × 5 × 10 = 2,500,000
2,500,000 / 100 = 25,000
So, the simple interest is $25,000
Next, we can find the total amount to be paid back after 10 years:
Total amount = P + SI
50,000 + 25,000 = 75,000
Therefore, Tom has to repay a total of $75,000 to the bank after 10 years.
Sara borrowed $45,500 for 24 months at 10% per annum. Find the simple interest she will need to pay.
$9100
The formula for finding the simple interest is:
SI = P × R × T / 100
Here, P= $45,500
R = 10%
T - 24 months
Here, we need to convert 24 months into years.
24 / 12 = 2 years
Now, we can substitute the values:
SI = 45,500 × 10 × 2 / 100
910000 / 100 = 9,100
Therefore, the simple interest Sara needs to pay is $9,100.
How much money was invested at 4% annual simple interest for 4 years to earn $36,000?
$225,000
Here, SI = $36,000
R = 4%
T = 4 years
We have to find the principal amount (P);
So, the formula will be like:
P = SI × 100 / R × T
P = 36,000 × 100 / 4 × 4
3,600,000 / 16 = 225,000
Hence, to earn $36,000 in interest at 4% per year over 4 years, the initial payment was $225,000.
Miya lends $2000 to Eliz at an interest rate of 5% per annum, compounded half-yearly for a period of 2 years. Find how much amount she gets after a period of 2 years from Eliz.
$2207.60
Here, the interest is compounded half-yearly. So, the formula will be:
A = P (1 + R / 100n) nT
Where, P = $2000
R = 5%
T = 2 years
n = 2 (half-yearly)
Let us substitute the values to the formula:
A = 2000 (1 + 5 / 100 × 2) 2× 2
A = 2000 (1+ 5 / 200) 4
A = 2000 (1 + 0.025) 4 = 2000 × (1.025) 4
(1.025) 4 = 1.1038
So, A = 2000 × 1.1038 = 2207.60
Therefore, Miya will receive $2207.60 from Eliz after 2 years.
Loki invests $6000 in a savings account with an annual interest rate of 3% compounded annually. How much will he have after 3 years?
$6556.36
The interest is compounded annually, so the formula will be:
A = P (1 + R/100) T
Here, P = $6000
R = 3%
T = 3
Now, we can substitute the values:
A = 6000 (1 + 3 / 100) 3
A = 6000 (1.03)3
(1.03)3 = 1.092727
Next, multiply by the principal (P):
A = 6000 × 1.092727
A = 6556.36
Hence, after 3 years, Loki will have $6556.36 in his savings account.
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Dr. Sarita Tiwari is a passionate educator specializing in Commercial Math, Vedic Math, and Abacus, with a mission to make numbers magical for young learners. With 8+ years of teaching experience and a Ph.D. in Business Economics, she blends academic rigo
: She believes math is like music—once you understand the rhythm, everything just flows!