COMPOUND INTEREST
Meaning of Interest
When you put your money in the bank or borrow money from someone, the money can increase over time.
That extra money you gain or pay is called interest.
There are two main types of interest:
- Simple Interest – The interest is always calculated on the original amount (the money you first put or borrowed).
- Compound Interest – The interest is calculated on the new total after each time period (for example, after each year).
Meaning of Compound Interest
Compound Interest is the interest that is calculated not only on the original money (called the Principal),
but also on the interest that has already been earned in the previous years.
In simple words: Interest on Interest!
Let us think of it like this — imagine you put ₦1,000 in the bank.
After one year, the bank gives you ₦100 as interest.
Now you have ₦1,100.
Next year, the bank gives you interest again — but this time, not just on ₦1,000,
it gives interest on ₦1,100.
That means your money grows faster every year!
Important Words to Know
- Principal (P): The original money you deposit or borrow.
- Rate (R): The percent (%) the bank uses to calculate interest per year.
- Time (T): The number of years the money is kept or borrowed.
- Amount (A): The total money after interest is added.
- Compound Interest (C.I): The extra money gained or paid — found by subtracting the principal from the amount.
Formula for Compound Interest
The formula for finding the total Amount (A) after compound interest is:
A = P × (1 + R/100)T
Then, to find the Compound Interest:
Compound Interest = A − P
Let’s Go Step by Step with Examples
Example 1:
Find the amount and compound interest on ₦1,000 for 2 years at 10% per annum.
- Step 1: Write down what we know.
P = ₦1,000, R = 10%, T = 2 years.
- Step 2: Use the formula:
A = P × (1 + R/100)T
- Step 3: Substitute the values:
A = 1,000 × (1 + 10/100)²
A = 1,000 × (1.1)²
- Step 4: (1.1)² = 1.21
So, A = 1,000 × 1.21 = ₦1,210.
- Step 5: Find the compound interest:
C.I = A − P = 1,210 − 1,000 = ₦210.
Answer: Amount = ₦1,210, Compound Interest = ₦210.
Example 2:
Find the compound interest on ₦2,000 for 3 years at 5% per year.
- Step 1: P = ₦2,000, R = 5%, T = 3 years.
- Step 2: A = P × (1 + R/100)T
- Step 3: A = 2,000 × (1 + 5/100)³ = 2,000 × (1.05)³
- Step 4: (1.05)³ = 1.157625
- Step 5: A = 2,000 × 1.157625 = ₦2,315.25
- Step 6: Compound Interest = A − P = 2,315.25 − 2,000 = ₦315.25
Answer: Amount = ₦2,315.25, C.I = ₦315.25
Example 3:
Find the compound interest on ₦5,000 for 2 years at 20% per annum.
- P = ₦5,000, R = 20%, T = 2 years.
- A = 5,000 × (1 + 20/100)² = 5,000 × (1.2)²
- (1.2)² = 1.44
- A = 5,000 × 1.44 = ₦7,200
- C.I = 7,200 − 5,000 = ₦2,200
Answer: Amount = ₦7,200, C.I = ₦2,200
Example 4:
Find the amount on ₦8,000 for 3 years at 10% compound interest.
- P = ₦8,000, R = 10%, T = 3 years.
- A = 8,000 × (1 + 10/100)³ = 8,000 × (1.1)³
- (1.1)³ = 1.331
- A = 8,000 × 1.331 = ₦10,648
- C.I = 10,648 − 8,000 = ₦2,648
Answer: Amount = ₦10,648, C.I = ₦2,648
Example 5:
Find the compound interest on ₦10,000 for 4 years at 5% per year.
- P = ₦10,000, R = 5%, T = 4 years.
- A = 10,000 × (1 + 5/100)⁴ = 10,000 × (1.05)⁴
- (1.05)⁴ = 1.21550625
- A = 10,000 × 1.21550625 = ₦12,155.06
- C.I = 12,155.06 − 10,000 = ₦2,155.06
Answer: Amount = ₦12,155.06, C.I = ₦2,155.06
Step-by-Step Understanding
- The bank uses your principal to calculate interest each year.
- After each year, the new total becomes the new principal.
- The interest keeps growing because you earn interest on both your money and the previous interest.
- That is why compound interest is more than simple interest when time increases.
Real-Life Uses of Compound Interest
- In banks – when you save money in a fixed deposit account.
- In loans – when people borrow money and the bank adds interest on top of the old interest.
- In investments – when your money grows faster every year.
- In business – when profit is reinvested and earns more profit.
Summary
- Compound Interest means interest added on both the original money and the interest earned before.
- Formula: A = P(1 + R/100)T
- Compound Interest = A − P
- Compound Interest grows faster than Simple Interest.
- Used in banks, savings, loans, and investments.
