In this lesson, you will be introduced to the simple interest earned by borrowing and the concept of borrowing. You will also be introduced to terms like principal, amount, interest rate and time period. Through these terms, using the simple interest formula, you can calculate the simple interest .
What is simple interest?
Simple interest is a quick and easy way to calculate interest on money, in the simple interest method the interest is always applied to the original principal amount, with the same interest rate for each cycle. When we invest our money in a bank, the bank gives us interest on our amount. There are several types of interest charged by banks, one of them being simple interest. Now, before going deep into the concept of simple interest, let us first understand what is the meaning of loan.
A loan is an amount that a person borrows from a bank or financial authority to meet his needs. Examples of loans include home loans, car loans, education loans and personal loans. A loan amount is required to be returned by the individual to the authorities on time, along with an additional amount, which is usually the interest you pay on the loan.
Simple Interest Formula
Simple interest is calculated by multiplying the interest rate by the time period and the principal. Time is usually in years. S.I. The formula is given as:
Simple Interest (SI) = P × T × R ⁄ 100 |
After the calculation for S.I. is done, the principal has to be added to it to get the total amount that the borrower has to give or the lender will collect. This is called total amount and its formula is given as:
A = P + S.I. |
Notations in S.I. Formula:
S.I. | Simple Interest |
P | Principal Amount |
A | Total Amount |
R | Rate of Interest |
T | Time (in Years) |
Simple interest is calculated with the following formula: SI = P × R × T, where P = principal, R = % interest rate per year, and T = time, usually calculated as the number of years. . The interest rate percentage is in r% and is to be written as r/100.
- Principal: The principal is the amount that was initially borrowed or invested from the bank. The principal is denoted by P.
- Rate: Rate is the interest rate at which the principal is lent to someone for a certain period of time, the rate of interest can be 5%, 10% or 13% etc. The rate of interest is represented by R.
- Time: Time is the period for which the principal is paid to someone. Time is denoted by t.
- Amount: When a person takes a loan from the bank, he has to return the principal amount borrowed and the interest amount, and this is called the total amount repaid.
Amount = Principal + Simple Interest
A = P + S.I.
A = P + PRT
A = P(1 + RT)
Simple Interest Example:
Rajesh’s father had borrowed $1,000 from the bank and the interest rate was 5%. What will be the simple interest if the amount is borrowed for 1 year? Similarly, calculate the simple interest if the amount is borrowed for 2 years, 3 years and 10 years?
Solution:
Principal Amount = $1,000, Rate of Interest = 5% = 5/100. (Add a sentence here describing the given information in the question.)
Simple Interest | |
1 Year | S.I = (1000 ×5 × 1)/100 = 50 |
2 Year | S.I = (1000 × 5 × 2)/100 = 100 |
3 Year | S.I = (1000 ×5 × 3)/100 = 150 |
10 Year | S.I = (1000 × 5 × 10)/100 = 500 |
Now, we can also prepare a table for the above question adding the amount to be returned after the given time period.
Simple Interest | Amount | |
1 Year | S.I = (1000 ×5 × 1)/100 = 50 | A= 1000 + 50 = 1050 |
2 Year | S.I = (1000 ×5 × 2)/100 = 100 | A= 1000 + 100 = 1100 |
3 Year | S.I = (1000 × 5 × 3)/100 = 150 | A = 1000 + 150 = 1150 |
10 Year | S.I = (1000 × 5 × 10)/100 = 500 | A = 1000 + 500 = 1500 |
Example Question S.I. based on formula
Question: If the principal amount is Rs. If so, calculate the simple interest. 2000, the time period is 1 year and the rate is 10%. Also, calculate the total amount at the end of 1 year.
Solution:
According to the formula for simple interest we have,
SI = [(Principal (P) × Time (T) × Rate (R)) / 100]
So, from the above values,
Simple Interest = [(2000 × 1 × 10)] / 100
= 20000/100
=200
So, the simple interest at the end of 1 year is Rs. 200.
For amount after 1 year,
A = P + S.I.
So, A = 2000+200 = 2200
Hence, the total amount at the end of the given tenure (i.e. 1 year) will be Rs. 2200.
What Types of Loans use Simple Interest?
Most banks these days apply compound interest on loans because this way banks get more money from their customers as interest, but this method is more complicated and difficult to explain to customers. On the other hand, the calculation becomes easier when banks apply simple interest methods. Simple interest is very useful when a customer wants a loan for a short period of time, for example, one year, two years, 1 month, 2 months or 6 months.
When one goes for a short-term loan using simple interest, the interest is applied on a daily or weekly basis instead of on an annual basis. Let’s say you borrowed $10,000 at 10% per annum simple interest, so this 10% per year rate divided by the per day rate equals 10/365 = 0.027%. So you have to pay an additional $2.73 per day on $10,000.
Simple Interest Calculator A = P(1 + rt)
Simple Interest Formulas and Calculations:
Using this simple interest calculator, to find the final investment value, A, using the simple interest formula: A = P(1 + rt) where P, T will be the number of times the investment is invested at r% interest rate per period. is the principal amount to be paid. of time period. where r is in decimal form; r = r / 100; r and t are in the same unit of time.
The accrued amount of an investment is P plus accumulated simple interest, I = Prt, so we have:/
A = P + I = P + (Prt), and finally A = P(1 + rt)
- Calculate Total Amount Accrued (Principal + Interest), solve for A
- A = P(1 + rt)
- Calculate Principal Amount, solve for P
- P = A / (1 + rt)
- Calculate rate of interest in decimal, solve for r
- r = (1/t)(A/P – 1)
- Calculate rate of interest in percent
- R = r * 100
- Calculate time, solve for t
- t = (1/r)(A/P – 1)
NCERT Solutions for Class 10 Maths Chapter 3 Ex 3.3
NCERT Solutions for Class 10 Maths Chapter 2
NCERT Solutions for Class 10 Maths Chapter 3
Simple Interest Vs Compound Interest
Simple interest and compound interest are the two ways to calculate the interest on the loan amount. It is believed that compound interest is more difficult to calculate than simple interest due to some fundamental differences between the two. Let us understand the difference between simple interest and compound interest through the table given below:
Simple Interest | Compound Interest |
Simple interest is calculated on the original principal amount every time. | Compound interest is calculated on the accumulated sum of principal and interest. |
It is calculated using the following formula: S.I.= P × R × T | It is calculated using the following formula: C.I.= P × (1+r)^{t }– P |
It is equal for every year on a certain principal. | It is different for every span of the time period as it is calculated on the amount and not principal. |
Simple Interest: Tips and Tricks
- To determine the time period, the day on which the money is borrowed is not counted, but the day on which the money is to be returned is counted.
- The interest rate is the interest on every $100 for a specified time period.
- The interest is always higher in case of compound interest as compared to simple interest.
- The formulas or methods for calculating compound interest are derived from simple interest calculation methods.
- The interest rate in the formula is always kept in fractions.
Think tank:
- What if a bank offers you interest in such a way that your money doubles every day, if you invest $1 in 1 day, in how many days will you become a billionaire?
- Would you invest if a bank offered a negative interest rate?
General interest
Who benefits from simple interest loan?
Since simple interest is often calculated on a daily basis, it mostly benefits those consumers who pay their bills or loans on time or at the beginning of every month.
Under the student-loan scenario above, if you sent a $300 payment on May 1, $238.36 goes toward principal. If you sent that same payment on April 20, $258.91 goes toward principal. If you can make early payments each month, your principal amount declines faster, and you pay off the loan sooner than the original estimate.
Conversely, if you pay off the loan late, your overpayment goes toward interest, if you make payments on time. Using the same automobile loan example, if your payment is due on May 1 and you make it on May 16, you are charged 45 days of interest at a cost of $92.46. This means that out of your $300 payment, only $207.54 goes toward principal. If you make frequent late payments over the life of a loan, your final payment will be larger than the original estimate because you didn’t pay the principal at the expected rate.
What types of loans use simple interest?
Simple interest is usually applied to automobile loans or short-term personal loans.
The compounding feel comes from varying principal payments — that is, the percentage of your mortgage payment that’s actually going toward the loan itself, not interest. Interest does not compound; principal pay. A $1,000 principal payment saves interest on that $1,000 and results in a higher principal payment the next year, and higher the next year, and so on. If you do not allow the principal payment to vary, as in an interest-only loan (zero principal payment), or by equalizing the principal payment, the loan interest itself does not compound. Lowering the interest rate, shortening the loan term, or prepaying the principal also has a compounding effect.1
Take bi-weekly mortgage payment plans, for example. Bi-weekly plans typically help consumers pay off their mortgages early because borrowers make two additional payments a year, saving interest over the life of the loan by paying off the principal faster.
If you are looking to take out a short-term personal loan, a personal loan calculator can be a great tool to determine the interest rate within your means in advance.
Simple Interest Vs Compound Interest
Interest can be either simple or compound. Simple interest is based on the principal principal amount of the loan or deposit.
Compound interest, on the other hand, is based on the principal amount and the interest accrued on it every tenor. Simple interest is calculated only on the principal amount, so it is easier to determine than compound interest.
In real-life situations, compound interest is often a factor in business transactions, investments, and financial products intended to span multiple periods or years. Simple interest is mainly used for simple calculations: they are usually for a single period or less than one year. Simple interest also applies to open-ended situations, such as credit card balances.
Why is simple interest “simple”?
“Simple” interest refers to the direct credit of cash flows associated with certain investments or deposits. For example, 1% annual simple interest would credit $1 for every $100 invested, year after year.
Which will pay more over time, simple or compound interest?
Compound interest will always pay off more after the first payment period. Let’s say you borrow $10,000 as a lump sum over three years with the principal plus interest at 10% annual interest. Using a simple interest calculation, 10% of the principal balance is added to your repayment amount every three years. This comes out to $1,000 per year, which adds up to $3,000 in interest over the life of the loan. At the time of repayment, the amount due is $13,000. Now suppose you take the same loan with the same terms, but the interest is compounded annually. When the loan is due, instead of owed $13,000, you end up with $13,310 due. While you might not consider $310 to be a huge difference, this example is just a three-year loan; Compound interest piles up and becomes oppressive with longer loan terms.
What are some financial instruments that use simple interest?
Most coupon-paying bonds use simple interest. So do most personal loans, including student loans and auto loans, and home mortgages.
What are some financial instruments that use compound interest?
Most bank deposit accounts, credit cards and some lines of credit use compound interest.