What is Simple Interest?
You may have sometimes borrowed money or stuff from some friend of yours or lent money to someone. In most cases, we do not charge a fee for lending money to the people we know but in the real world, money is not borrowed or lent for free. Banks and other financial institutions charge a fee for lending us money. On the other hand, they pay us a fee if we lend them money by depositing it in a bank account. This fee is known as simple interest. Banks pay us interest for depositing money in our bank accounts, and they charge interest for loans.
Simple interest depends on three factors: the amount that is being used, the time period, and the rate of interest. The amount of money in usage, that is the amount that is deposited in the bank or the amount that is borrowed, is known as the principal. Time period of a transaction is the duration for which the money is being used. The annual interest rate or rate of interest is a percent that acts on the principal which gives us the interest incurred.
How to Calculate Simple Interest
Simple interest can be calculated using the following formula:
We multiply the principal amount, rate of interest (in decimal form), and time period to find the simple interest.
For example, if a person borrows $1000 from a bank at an interest rate 5% for 5 years, the interest will be:
P = $1000
r = 5% \(=\frac{5}{100}=0.05\)
t = 5 years
I = Prt
= \(1000\times0.05 \times 5\)
I = $250
So, the interest is $250.
Calculating the Balance
You can calculate the bank balance you will have after a certain number of years if you know the money deposited in your bank account and the interest rate offered by your bank.
For example, if you deposit $350 in your bank account and your bank offers an interest rate of 4% per annum, you can calculate the balance you will have in 10 years.
The money you have in your bank account = $350
Duration of deposit = 10 years
\(\text{Rate of interest}=4\)% = \(\frac{4}{100}=0.04\)
I = Prt
= \(350\times 0.04\times 10\)
= $140
You will get an interest of $140 in 10 years.
Your bank balance after 10 years = Principal amount + Interest
= 350 + 140
= $490
So, the bank balance after 10 years will be $490.
Calculating Annual Interest Rate
You can use the same equation to find the annual interest rate of a transaction. In this case, you will need to know the principal amount, the simple interest, and the time period.
The original equation is I = Prt
So, the rate of interest can be calculated by dividing the simple interest by the product of the principal amount and the time period.
We can rearrange this equation to get \(r=\frac{I}{Pt}\)
To express the annual interest rate as a percent: \(r=\frac{I}{Pt}\times 100\)
For example, if you receive $192 as interest for depositing $800 in a period of 6 years, the interest rate can be calculated as follows:
I = Prt
\(r=\frac{I}{Pt}\)
\(r=\frac{192}{800\times 6}=0.04\times 100=4\)%
So, the annual interest rate is 0.04 or 4%.
Finding the Amount of Time
We can find the time period by rearranging the terms in the same equation.
I = Prt
\(t=\frac{I}{PR}\)
For example, if you need to find the time required to get an interest of $1400 on a principal amount of $2000 at an interest rate of 7%, we can use the following formula.
\(t=\frac{I}{PR}\)
\(=\frac{1400}{2000\times 0.07}\)
= 10 years
Hence, it will take 10 years to get an interest of $1400.
Solved Simple Interest Examples
Example 1: Jamie deposited $900 in his bank account and waited for 2 years. Find the account balance if the interest rate offered by the bank is 7%.
Solution:
To find the bank balance at the end of 2 years, calculate the simple interest and add it to the principal.
I = Prt
\(I=900\times 0.07\times 2\)
\(=9\times 7\times 2\)
= $126
So, simple interest is $126
Bank balance = Principal amount + simple interest
= $900 + $126
= $1026
Example 2: Bella borrowed $15,000 to buy a car. If she has to pay a total simple interest of $3000 at the end of 5 years, find the rate of interest at which she took the loan.
Solution:
We can find the rate of interest by rearranging the terms in the simple interest equation.
I = Prt
\(r=\frac{I}{Pt}\)
\(=\frac{3000}{15,000\times 5}\)
\(=\frac{3}{15\times 5}\)
\(=\frac{1}{5\times 5}\)
\(=\frac{1}{25}=0.04\times 100=4\)%
Therefore, Bella borrowed the money at a rate of interest of 4% per annum.
Example 3: Joshua deposited $8000 in a bank at a rate of 6% per annum. Find the time period in which the interest will add up to $2400.
Solution:
Principal amount = $8000
Simple interest = $2400
Rate of interest \(=6\)% = \(\frac{6}{100}=0.06\)
I = Prt
\(t=\frac{I}{Pr}\)
\(=\frac{2400}{8000\times 0.06}\)
\(=\frac{240}{8\times 6}\)
\(=\frac{240}{48}=5~\text{years}\)
Therefore, it will take 5 years for the interest to add up to $2400.
Example 4: The yearly balance of a bank account is given in the table. What is the interest rate of the account? Find the bank balance after 15 years.
Solution:
The balance is the amount we get after adding the interest to the principal. So if no interest has been incurred, that is if the principal has not even completed a year of deposit, then the balance is simply the principal itself.
Hence initially (when year = 0), the principal = balance = $1200.
So, Principal P = $1200
The account balance after 1 year is $1332.
Balance amount = Principal amount + Simple interest
Simple interest = Balance amount – Principal amount
I = $1332 – $1200 = $132
So, the interest at the end of the first year is $132.
We can find the rate of interest from the information available to us.
I = Prt
\(r=\frac{I}{Pt}\)
\(=\frac{132}{1200\times 1}=0.11\times 100=11\)%
Therefore, the rate of interest is 11%.
Now, we can find the account balance at the end of 15 years.
I = Prt
\(=1200\times 0.11\times 15\)
= $1980
Therefore, the simple interest earned in 15 years is $1980.
Balance amount = Principal amount + Simple interest
In Simple interest calculations, the principal remains constant.
Balance amount = $1200 + $1980 = $3180
So, the account balance after 15 years will be $3180.
Per annum means each year. For example, Jane receiving $400 per annum means that Jane receives $400 every year.
Simple interest is calculated on the principal for a fixed rate of interest and not on the balance (principal + interest). That is, the simple interest incurred for different years varies only according to the number of years, the interest rate and the principal remains the same. Hence, the principal for a particular simple interest calculation, no matter the number of years, is always the same.
It is a method of calculating interest on the money that is lent or borrowed. It is the product of principal amount, rate of interest, and time period.
Simple interest I = Prt