Home / United States / Math Classes / Formulas / Simple Interest Formulas

Unlike a couple of centuries ago, the world’s economy is on a steep climb. This rapid development was sparked by easy access to money in the form of loans. But access to money comes at a cost. Here we will learn how to calculate the interest that is paid to a depositor or the interest paid by the borrower. ...Read MoreRead Less

Interest is the money paid for borrowing money or the cost charged for lending money. Banks charge interest from people for borrowing money in the form of loans and they pay interest to people who deposit money in bank accounts or fixed deposits. Interest can be calculated in various methods. Simple interest is a type of interest that is calculated on the principal amount of money.

We have two formulas associated with simple interest. We use one formula to calculate just the interest amount. The second formula is used to calculate the total amount, which is the sum of the principal amount and the interest.

- Simple Interest = Prt
- Amount = P(1+rt)

To calculate the simple interest, you need to know the principal amount, rate of interest and the time duration. The principal amount (P) is the original amount you borrowed from the bank as a loan or lent to the bank as a deposit. The rate of interest (r) is the percentage of the principal amount charged as interest, usually on an annual basis. But, *r* is usually expressed as decimals. That means we write *r* as 0.1 for a 10% interest rate. The duration of time that you take to pay back the money is known as the time period (t) of the loan. The time period can be months or years. In most cases, interest is calculated annually. Hence, we express the time period in years.

Where,

P = Principal amount

r = Rate of interest

t = Time period

If you want to calculate the total amount directly, add the simple interest to the principal amount.

Amount = Principal amount + Simple interest

= P + Prt

= P(1+rt)

**Example 1:** Calculate the simple interest if the principal amount is $10,000, the rate of interest is 5%, and the time period is 3 years.

**Solution:**

P = $10,000

r = 5% or 0.05

t = 3 years

Simple interest = Prt

= \(10,000\times 0.05\times 3\)

= \(500\times 3\)

= $1500

So, the simple interest in this case is $1500.

**Example 2:** Calculate the total amount of money to be paid back for a loan of $3500 at an interest rate of 8% over a period of 5 years.

**Solution:**

P = $3500

r = 8% or 0.08

t = 5 years

Amount to be paid back = P(1+rt)

= \(3500\times(1 + 0.08\times 5)\)

= \(3500\times (1 + 0.4)\)

= \(3500\times 1.4\)

= $4900

Therefore, the total amount to be paid back in 3 years is $4900.

**Example 3:** Marlin took a loan of $30,000 to pay for his higher education. If the interest rate is 12%, find the total amount he needs to pay back in 6 years.

**Solution:**

P = $30,000

r = 12% or 0.12

t = 6 years

Amount to be paid back = P(1+rt)

= \(30,000\times (1+0.12\times 6)\)

= \(30,000\times (1+0.72)\)

= \(30,000\times 1.72\)

= $51,600

Therefore, Marlin needs to pay back a total amount of $51,600 in 6 years.

**Example 4:** Sara deposited $5200 in her bank account. The bank offers simple interest at the rate of 3% for the money deposited in the account. If she doesn’t make any transactions with the money in the account, how much money will she have after 6 years?

**Solution:**

The amount deposited by Sara (P) = $5200

Interest rate paid by the bank (r) = 3% or 0.03

Time period (t) = 6 years

The total amount in Sara’s account after 6 years = P(1 + rt)

= $\(5200\times (1+0.036)\)

= $\(5200\times (1+0.18)\)

= $\(5200\times 1.18\)

= $6136

Therefore, Sara will have $6136 in her bank account after 6 years.

Frequently Asked Questions

Interest is the fee paid for the usage of money. A borrower pays interest to the lender and a depositor gets paid interest by financial institutions for depositing money.

Simple interest is one of many methods used for calculating interest. In this method, the interest is charged on the principal amount.

Simple interest is the product of the principal amount, rate of interest, and time period. That is Simple interest = Prt

The initial amount that is borrowed or deposited is known as the principal amount. If you take a loan of $3000, then that is the principal amount.

The interest rate is generally expressed as a percentage but during calculations, we use the decimal value of the interest rate. If you want to use the percentage value, divide the simple interest equation by 100. So, the equation becomes:

Simple interest = \(\frac{\text{Prt}}{100}\) where r is expressed in percent.

Now that you have learned about simple interests, go ahead and check out these concepts: