Simple interest is one of the easiest topics in mathematics once you understand what each number in the question means.

You can use simple interest to calculate the interest earned on savings, the interest charged on a loan, or the total amount that will be paid or received after a certain period.

The main formula is straightforward

Simple Interest = (Principal × Rate × Time) ÷ 100

But knowing the formula is only half the job. You also need to know how to identify the principal, interest rate, and time, and how to handle questions where one of these values is missing.

This easy post explains everything step by step on how to Calculate Simple Interest Step by Step, with worked examples and practice questions.

What is simple interest?

Simple interest is interest calculated only on the original amount of money.

The original amount is called the principal.

Unlike compound interest, simple interest does not add previously earned interest back to the amount used to calculate the next interest.

For example, if you invest ₦100,000 at a simple interest rate of 10% per year, the interest is calculated from the original ₦100,000 each year.

The interest earned each year would therefore remain the same.

The simple interest formula

The formula for calculating simple interest is

SI = (P × R × T) ÷ 100

where

SI means simple interest

P means principal

R means rate of interest per year

T means time in years

You may also see the formula written as

SI = PRT/100

Both forms mean exactly the same thing.

What is the principal?

The principal is the original amount of money borrowed, invested, or saved.

For example, if you put ₦50,000 into a savings account, your principal is

₦50,000

If you borrow ₦200,000, the principal is

₦200,000

The principal is usually the amount given at the beginning of the question.

What is the rate?

The rate is the percentage charged or earned.

For example, if a question says

“An investment earns simple interest at 8% per year”

the rate is

8%

If it says the interest rate is 12% per annum, the rate is

12%

The word per annum simply means per year.

What is the time?

Time tells you how long the money is borrowed, invested, or saved.

For the standard simple interest formula, time is normally expressed in years.

For example

2 years means T = 2

5 years means T = 5

6 months means T = 1/2 year

3 months means T = 1/4 year

This is important because using months directly in the formula when the rate is an annual rate will give you the wrong answer.

How to calculate simple interest

Follow these steps

Step 1 Identify the principal.

Step 2 Identify the interest rate.

Step 3 Convert the time to years if necessary.

Step 4 Substitute the values into the simple interest formula.

Step 5 Calculate the interest.

Let’s work through some examples.

Example 1 Calculate simple interest on ₦100,000

A person invests ₦100,000 at a simple interest rate of 10% per year for 3 years. Calculate the simple interest.

First identify the values

P = ₦100,000

R = 10%

T = 3 years

Use the formula

SI = (P × R × T) ÷ 100

Substitute the values

SI = (100,000 × 10 × 3) ÷ 100

Multiply

100,000 × 10 × 3 = 3,000,000

Now divide by 100

SI = ₦30,000

Therefore, the simple interest is

₦30,000

Example 2 Calculate simple interest on ₦50,000

Calculate the simple interest on ₦50,000 at 6% per year for 4 years.

We have

P = ₦50,000

R = 6%

T = 4 years

Using

SI = (P × R × T) ÷ 100

we get

SI = (50,000 × 6 × 4) ÷ 100

SI = 1,200,000 ÷ 100

SI = ₦12,000

Therefore, the simple interest is

₦12,000

How to calculate the total amount after simple interest

Sometimes a question does not ask for the interest alone.

It may ask for the amount received or the total amount to be repaid.

The total amount is

Amount = Principal + Simple Interest

For example, suppose you invest ₦100,000 and earn ₦30,000 in simple interest.

The total amount is

₦100,000 + ₦30,000 = ₦130,000

So

Principal = ₦100,000

Simple Interest = ₦30,000

Total Amount = ₦130,000

This distinction is important.

If a question asks for the simple interest, give only the interest.

If it asks for the amount, add the interest to the principal.

Example 3 Find the amount

A man invests ₦200,000 at 5% simple interest per year for 3 years. Find the total amount after 3 years.

First calculate the interest.

P = ₦200,000

R = 5%

T = 3 years

SI = (200,000 × 5 × 3) ÷ 100

SI = ₦30,000

Now calculate the total amount

Amount = Principal + Interest

Amount = ₦200,000 + ₦30,000

Amount = ₦230,000

Therefore, the total amount is

₦230,000

How to calculate simple interest for months

This is where many students make mistakes.

If the interest rate is given per year, convert the time from months to years before using the formula.

There are 12 months in one year.

Therefore

6 months = 6/12 = 1/2 year

3 months = 3/12 = 1/4 year

9 months = 9/12 = 3/4 year

Example 4 Simple interest for 6 months

Calculate the simple interest on ₦80,000 at 12% per year for 6 months.

The principal is

P = ₦80,000

The rate is

R = 12%

The time is 6 months.

Convert 6 months to years

T = 6/12 = 1/2 year

Now use the formula

SI = (80,000 × 12 × 1/2) ÷ 100

SI = ₦4,800

Therefore, the simple interest is

₦4,800

Example 5 Simple interest for 9 months

Calculate the simple interest on ₦120,000 at 8% per year for 9 months.

Convert 9 months to years

T = 9/12 = 3/4 year

Now substitute

SI = (120,000 × 8 × 3/4) ÷ 100

First calculate

120,000 × 8 = 960,000

Then

960,000 × 3/4 = 720,000

Divide by 100

SI = ₦7,200

Therefore, the simple interest is

₦7,200

How to calculate simple interest for days

Some questions give the time in days instead of years or months.

If the question uses a 365-day year, convert the number of days into years.

For example

90 days = 90/365 year

However, some mathematics questions may specify a different number of days in a year, such as 360 days.

Always follow the instruction given in the question.

Example 6 Simple interest for 90 days

Suppose ₦100,000 is invested at 12% simple interest per year for 90 days, using a 360-day year.

Convert the time to years

T = 90/360

T = 1/4 year

Now calculate

SI = (100,000 × 12 × 1/4) ÷ 100

SI = ₦3,000

Therefore, the simple interest is

₦3,000

How to find the principal when the simple interest is given

You may be given the interest, rate, and time and asked to find the original amount.

Start with

SI = PRT/100

Rearrange the formula to make P the subject

P = (SI × 100) ÷ (R × T)

Example 7 Find the principal

The simple interest on a sum of money at 5% per year for 4 years is ₦10,000. Find the principal.

We know

SI = ₦10,000

R = 5%

T = 4 years

Use

P = (SI × 100) ÷ (R × T)

Substitute

P = (10,000 × 100) ÷ (5 × 4)

P = 1,000,000 ÷ 20

P = ₦50,000

Therefore, the principal is

₦50,000

How to find the rate when the simple interest is given

Sometimes the principal, interest, and time are given, but the rate is missing.

Start with

SI = PRT/100

Rearrange to make R the subject

R = (SI × 100) ÷ (P × T)

Example 8 Find the interest rate

A sum of ₦40,000 earns ₦8,000 simple interest in 5 years. Find the rate.

We have

SI = ₦8,000

P = ₦40,000

T = 5 years

Therefore

R = (8,000 × 100) ÷ (40,000 × 5)

R = 800,000 ÷ 200,000

R = 4%

Therefore, the interest rate is

4% per year

How to find the time when the simple interest is given

You may also be asked to find how long the money was invested or borrowed.

Rearrange the simple interest formula

SI = PRT/100

to make T the subject

T = (SI × 100) ÷ (P × R)

Example 9 Find the time

A sum of ₦60,000 earns ₦12,000 simple interest at a rate of 10% per year. Find the time.

We have

SI = ₦12,000

P = ₦60,000

R = 10%

Therefore

T = (12,000 × 100) ÷ (60,000 × 10)

T = 1,200,000 ÷ 600,000

T = 2 years

Therefore, the money was invested for

2 years

Simple interest versus compound interest

Simple interest and compound interest are not the same.

With simple interest, the interest is calculated from the original principal.

With compound interest, interest can be added to the balance, meaning future interest may be calculated on both the original money and previously earned interest.

For example, if you invest ₦100,000 at 10% simple interest per year

After one year, the interest is ₦10,000.

After two years, the total simple interest is ₦20,000.

After three years, the total simple interest is ₦30,000.

The interest added each year stays the same because the calculation is based on the original ₦100,000.

A quick way to calculate simple interest

For some questions, you can make the calculation easier by finding the interest for one year first.

Suppose you invest ₦50,000 at 8% per year.

8% of ₦50,000 is

₦50,000 × 8/100 = ₦4,000

So the interest for one year is ₦4,000.

For 5 years

₦4,000 × 5 = ₦20,000

Therefore, the simple interest is

₦20,000

This shortcut works because simple interest remains based on the original principal.

Common mistakes when calculating simple interest

Using the total amount instead of the principal

The formula uses the original principal, not the final amount.

If the principal is ₦100,000 and the final amount is ₦120,000, use ₦100,000 in the simple interest formula.

Forgetting to convert months into years

If the rate is 12% per year and the time is 6 months, do not enter 6 as the time.

Use

6/12 = 1/2 year

Confusing interest with amount

Interest and total amount are different.

For example

Principal = ₦100,000

Interest = ₦20,000

Amount = ₦120,000

Forgetting the percentage sign

A rate of 10% means

10/100

not 10.

The formula already includes division by 100, so you can use 10 directly in

SI = PRT/100

Using the wrong time period

If the rate is quoted per year, make sure your time is in years.

If the rate is quoted per month, the time should normally be expressed in months.

The rate and time must use matching periods.

Simple interest word problem

Let’s look at a more complete example.

A trader borrows ₦500,000 from a lender at a simple interest rate of 8% per year for 2 years. Calculate the simple interest and the total amount the trader will repay.

First identify the values

P = ₦500,000

R = 8%

T = 2 years

Calculate the interest

SI = (500,000 × 8 × 2) ÷ 100

SI = ₦80,000

Now calculate the total amount

Amount = Principal + Interest

Amount = ₦500,000 + ₦80,000

Amount = ₦580,000

Therefore

Simple interest = ₦80,000

Total amount = ₦580,000

Notice that the question has two answers because it asks for both the interest and the amount.

Simple interest formula cheat sheet

If you know the principal, rate, and time

SI = PRT/100

If you know the simple interest and want the principal

P = SI × 100 / RT

If you want the rate

R = SI × 100 / PT

If you want the time

T = SI × 100 / PR

To find the total amount

A = P + SI

These formulas are useful when solving examination questions where one of the four main values is missing.

Practice questions on simple interest

Try these questions yourself before checking the answers.

Question 1

Calculate the simple interest on ₦100,000 at 5% per year for 3 years.

Question 2

Find the simple interest on ₦80,000 at 10% per year for 2 years.

Question 3

A sum of ₦50,000 is invested at 8% simple interest for 4 years. Find the total amount.

Question 4

Find the simple interest on ₦120,000 at 6% per year for 6 months.

Question 5

A sum of money earns ₦15,000 simple interest at 5% per year for 3 years. Find the principal.

Question 6

A sum of ₦40,000 earns ₦8,000 simple interest in 5 years. Find the rate.

Question 7

A sum of ₦60,000 earns ₦9,000 simple interest at 5% per year. Find the time.

Question 8

A person borrows ₦250,000 at 12% simple interest per year for 2 years. Find the simple interest and the total amount to be repaid.

Answers

1. ₦15,000

2. ₦16,000

3. ₦66,000

4. ₦3,600

5. ₦100,000

6. 4%

7. 3 years

8. Simple interest = ₦60,000. Total amount = ₦310,000.

Frequently asked questions about simple interest

What is the formula for calculating simple interest?

The formula is

SI = PRT/100

where P is the principal, R is the rate, and T is the time in years.

How do I calculate simple interest on a loan?

Multiply the original loan amount by the interest rate and the time, then divide by 100.

SI = PRT/100

If you need the total amount to repay, add the interest to the original loan amount.

How do I calculate simple interest for 6 months?

Convert 6 months into years.

6/12 = 1/2 year

Then use half a year as the time in the simple interest formula when the rate is an annual rate.

What is the difference between simple interest and compound interest?

Simple interest is calculated from the original principal throughout the period. Compound interest can be calculated on the principal plus previously accumulated interest.

What does per annum mean in simple interest?

Per annum means per year.

Therefore, an interest rate of 10% per annum means an interest rate of 10% per year.

How do I calculate the total amount after simple interest?

Add the simple interest to the principal.

Amount = Principal + Simple Interest

Can simple interest be used for loans?

Yes. Simple interest can be used to calculate the interest charged on a loan when the loan terms specify that interest is calculated using the simple interest method.

Final takeaway

The most important formula to remember is

SI = PRT/100

Before calculating, identify the principal, rate, and time.

If the time is given in months or days, convert it into the appropriate period so that it matches the rate.

Then calculate the simple interest and, if required, add it to the principal to find the total amount.

Once you understand what P, R, and T represent, simple interest questions become much easier to solve.