Simple Interest Problems

Simple interest is a topic where math connects with everyday situations. It helps us understand how money grows when we borrow or save it for some time. You might have heard people talk about interest in banks or loans, but the idea behind it is not very hard.

Think about this for a moment: if you lend money to a friend, would you expect the same amount back or a little extra after some time? That extra amount is called interest.

In this blog, we will learn how to calculate simple interest using a formula. We will also understand what each term means and how to use them in different problems.

Key Concepts

• Simple interest, percent of interest and principal.
• Find simple interest.
• Find the percent of interest.
• Find the principal.

Solve simple interest problems

What is principal?

When an individual or business borrows a certain sum of money through a loan, the amount borrowed is referred to as the principal amount.

Example: Maddy wants to construct his house; the estimation was calculated to be $40000. He decides to borrow $10000 from the bank. This borrowed amount is termed as principal.

What is simple interest?

Simple interest is the method of calculating the interest amount for a principal amount of money. We generally borrow money from our siblings or friends when our pocket money gets exhausted or lend money. We use that money for our purpose and return it when we receive the next month’s pocket money to them. This is how lending and borrowing work at home.

But in the real world, money is not free to borrow. We often borrow money from banks in the form of a loan. During payback, apart from the loan amount, we pay an extra amount that depends on the loan amount and the time period for which we borrowed. This additional amount being paid is called simple interest

What is a simple interest formula?

When we talk about simple interests, the first thing we need is the formula. This formula helps us find how much extra money is added after a certain time.

Here is how simple interest is calculated:

Simple Interest (SI) = (P × R × T) / 100

Here is what each letter means:

• P is the principal, or the starting amount
• R is the rate of interest per year
• T is the time, usually in years

If you look at it closely, the formula is quite direct. You multiply all three values and then divide by 100. One thing to remember is that simple interest is always calculated on the same principal. It does not change with time. So once you understand the formula, most questions become easier to handle.

Equation for Simple Interest

The same formula can also be written as an equation. This is useful when we need to find something other than interest.

SI = (P × R × T) / 100

In many questions, you may not get all the values. Sometimes the principal is missing, or the rate is not given. In such cases, we change the formula a little.

Here are some forms you should know:

• To find Principal (P)
  P = (SI × 100) / (R × T)
• To find Rate (R)
  R = (SI × 100) / (P × T)
• To find Time (T)
  T = (SI × 100) / (P × R)

You do not need to memorise all of them at once. With practice, you will start understanding how they are formed.

What is the percent of interest?

An interest rate is a percent used to calculate interest on the principal.

Example:

Maddy borrows $10000 at 4% interest for a period of two years.

Here, we understand that principal = $10000 and rate of interest = 4%. 

Let us understand, what does 4% mean?

4% is written as 4/100

The banker here wants to convey that if Maddy borrows $100, then he must pay $4 extra during the payback. 

Maddy here borrows $10000.

The interest to be paid is 10000 × 4% = 10000 × 0.04 = $400.

Therefore, Maddy must pay $400 during the payback additionally along with the principal of $10000.

Find simple interest

Example 1: Ann opens a savings account with a deposit of $670. She will earn 1.5% interest each year on her money. How much interest will she earn over a period of 10 years? (assuming she does not add or take out any money).

Solution:

Step 1:

Use the percent equation to find the amount of interest earned in one year.

We know that, part = percent × whole

Let us take the interest amount as I, part = I, percent = 1.5%, and whole = amount deposited.

I = 1.5% × 670

I = 0.015 × 670

I = $10.05

Step 2: Multiply the interest earned in one year by 10 to calculate the total interest Ann will earn over a 10-year period.

Total interest earned by Ann in 10 years = 10.05 × 10

                                                              = 100.5

Therefore, Ann gets $100.5 in ten years’ time.

Example 2: Dave borrows $1500 to repair his house. He will pay off the loan after 3 years by paying back the principal plus 3.5% interest for each year. How much will he pay in interest, and how much will she pack back altogether

Solution:

Step 1:

Use the percent equation to find the amount of interest earned in one year.

We know that, part = percent × whole

Let us take the interest amount as I, part = I, percent = 3.5% and whole = amount borrowed.

I = 3.5% × 1500

I = 0.035 × 1500

I = $52.5

Step 2: Multiply the interest to be paid in one year by 3 to calculate the total interest Dave will have to pay over a 3-year period.

Total interest in 3 years = 52.5 × 3

                                      = 157.5

Total amount to be paid back = principal + interest

                                                           = 1500 + 157.5

                                                           = 1657.5

Therefore, the interest to be paid by Dave is $157.5, and the total amount altogether is $1657.5

Find the percent of interest

Example 1: A bank lends $4000 on loan to a businessman in simple interest. If he promises to pay $20 every month for a period of two years. What is the interest rate on the loan per annum?

Solution:

Step 1:

Multiply the interest by 12 to get the interest for 1 year.

20 × 12 = $240

Interest to be paid in two years = 240 × 2

                                                   = $480.

Step 2: Use the percent equation to find the interest rate.

We know that, part = percent × whole

Here we understand that, part = interest, whole = principal and percent rate = p.

Let us take the interest rate as p, which we are about to find.

Interest = interest rate × principal.

480 = p × 4000

Divide the equation by 4000 on both sides.

480/4000 = p

p = 0.12

Express the decimal as a percent by multiplying by 100.

P = 12%.

Therefore, the interest rate levied on the loan by the bank is 12%.

Example 2: A person deposits $5000 in a bank in simple interest; he finds $6200 after two years in the account. What is the rate of interest per annum?

Solution:

Step 1:

Find the interest paid by the bank in those two years

Interest paid in two years = 6200 – 5000

                                          = $1200.

Interest paid in one year = 1200/2

Interest paid in one year = 600

Step 2: Use the percent equation to find the interest rate.

We know that, part = percent × whole

Here we understand that, part = interest, whole = principal and percent rate = p.

Let us take the interest rate as p, which we are about to find.

Interest = interest rate × principal.

600 = p × 5000

Divide the equation by 1200 on both sides.

600/5000 = p                       

p = 0.12

Express the decimal as a percent by multiplying by 100.

P = 12%.

Therefore, the interest rate levied on the deposit by the bank is 12%

How to Find Principal in Simple Interest

Example 1: Brit opened a savings account that fetches him 4% interest. Brit estimates that assuming he neither adds to nor withdraws from his account, he will earn $300 in interest after 5 years. How much did Brit deposit when he opened the account?

Solution:

Step 1:

Firstly, find the interest he earns in 1 year.

300 ÷ 4 = 75

Interest earned per year is $75.

Step 2: Use the percent equation to find the deposit or principal.

We know that, part = percent × whole

Let us take the principal as p, which we are about to find.

Here we understand that part = interest amount, whole = principal and percent = interest rate.

Interest amount per year = interest rate × principal.

75 = 4% × P

75 = 0.04 × P

Divide the equation by 0.04 on both sides.

75/0.04 = 0.04/0.04 =  × P

P × 1 =1875

P = $1875

Therefore, Brit deposits $1875 in the account at 4% simple interest to earn $300 interest over a period of 4 years.

Example 2: Alex borrowed money for school. He took out a loan that charges 5% simple interest. He will end up paying $800 in interest after 5 years. How much did Alex borrow for school?

Solution:

Step 1:

Firstly, find the interest he earns in 1 year.

800 ÷ 5 = 160

Interest earned per year is $160.

Step 2: Use the percent equation to find the deposit or principal.

We know that, part = percent × whole

Let us take the principal as p, which we are about to find.

Here we understand that, part = interest amount, whole = principal and percent = interest rate.

Interest amount per year = interest rate × principal.

160 = 5% × P

160 = 0.05 × P

Divide the equation by 0.05 on both sides.

160/0.05 = 0.05/0.05 =  × P

P × 1 =3300

P = $3300

Therefore, Alex borrows $3300 for school at 5% simple interest over a period of 5 years and pays $800 interest.

Simple Interest vs Compound Interest

Students often get confused between simple interest and compound interest. They are related, but they do not work in the same way.

Key Differences

Basis	Simple Interest	Compound Interest
Calculation	Only on principal	On principal and interest
Interest each year	Same	Keeps changing
Growth	Slow and steady	Faster over time
Formula	SI = (P × R × T) / 100	CI = P(1 + R/100)^T – P
Where used	Basic loans	Banks, savings

Explanation

In simple interest, the interest is always taken on the starting amount. So if the principal is $1000, the interest is calculated on $1000 every year.

That is why the interest stays the same.

In compound interest, things work differently. The interest gets added to the principal. Next time, interest is calculated on this new total. So the amount keeps increasing year after year. For example:

• Simple interest gives the same increase every year
• Compound interest gives a bigger increase each year

This is why banks prefer compound interest for savings and investments.

Solved Simple Interest Practice Problems

Let us solve a few problems together.

Problem 1

Find the simple interest on $2000 for 3 years at 5%.

Solution:

SI = (2000 × 5 × 3) / 100
SI = 300

So, the interest is $300.

Problem 2

Find the total amount if $1500 is borrowed at 4% for 2 years.

Solution:

First find interest:
SI = (1500 × 4 × 2) / 100 = 120

Now add to principal:
Total amount = 1500 + 120 = $1620

Problem 3

A sum earns $90 in 3 years at 3%. Find the principal.

Solution:

P = (90 × 100) / (3 × 3)
P = 9000 / 9
P = $1000

Exercise

The following are a few questions in simple interest, that you can practice: 

1. A bank lends $1000 at 2.5% in simple interest. After 5 years, how much money should be paid back to the bank?
2. Adam borrows $6600 from his friend at 1.5% in simple interest; he promises to pay it back in 3 years. How much interest does he pay?
3. Calculate the interest earned on lending $500 for two years at 3% per annum in simple interest?
4. Greg pays $100 in interest per year for 8 years for borrowing $12000 in simple interest; what is the interest rate?   
5. A bank asks to pay $50 per year for 2 years on borrowing $1000. Determine the rate of interest.
6. A company lends Maya $4000. Every month she will pay $11.88 interest for 1 year. What is the interest rate?
7. The interest earned at 2% is $320 for 2 years. What is the principal?
8. The interest earned at 5% is $1000 for a period of 10 years. Determine the principal.
9. Rebecca borrows money to pay for her medical expenses. She paid $400 over a period of 10 years borrowing at 2% in simple interest. How much did she borrow?
10. Adam decided to deposit $8000 in a bank at a simple interest of 3% till 12 years so that he can use it for his business expansion later. How much money will he have in his account after 12 years, assuming that he neither draws nor adds any amount?

What have we learned?

• Understanding simple interest, percent of interest and principal.
• Finding simple interest.
• Finding the percent of interest.
• Finding the principal.

Conclusion

Simple interest is one of those topics that becomes easy once the formula is clear in your mind. Most questions follow the same pattern. You just need to identify what is given and what you have to find. Try solving a few questions daily. With time, you will notice that you need less effort to solve them.

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