Rajesh has borrowed Rs 27000 at 20 per annum Compound Interest and paid back Rs 46656

Simple interest is a way of calculating the amount of interest charged on a sum at a particular rate and during a specified time period. In comparison to compound interest, which adds the interest of previous years’ principal to compute the interest of the current year, the principal amount in simple interest is always the same. A loan is a sum of money borrowed from a bank or financial institution to meet one’s requirements. Home loans, vehicle loans, student loans, and personal loans are some kinds of loans. A loan amount is needed to be repaid to the authorities on time plus an additional amount, which is generally the interest you pay on the loan.

Simple Interest Formula 

Simple interest is a quick and straightforward method to calculate interest on money. In the simple interest method, interest is always applied to the original principal amount, with the same rate of interest for each time cycle. When we put our money in a bank, we get interested in it. Banks charge a variety of interest rates, one of which is simple interest. The formula to calculate Simple Interest is,

S.I = P × R × T 

Here, 

• p represents Principal 
• r represents the Rate of Interest in % per annum . r % it also can be written as r/100.
• t represents the Time duration for which the interest has been calculated as the number of years. 

• Principal: The principal is the amount borrowed or invested from the bank. The principal is symbolized by the letter “P”.
• Rate: The rate of interest at which the principal amount is handed to someone for a specific period of time. 
  For Example, the rate of interest can be 5%, 10%, or 13%. Here the interest rate can be represented by “r”.
• Time: The duration during which the principal sum is handed to someone is referred to as time.  Time is symbolized by “T”.
• Amount: When a person acquires a loan from a bank, he or she is required to repay the principal borrowed plus the interest amount, and the total amount repaid is referred to as the Amount.

Therefore,

Amount = Principal + Simple Interest

= P(1 + RT)                   

Sample Questions 

Question 1:  Rajesh takes a loan of Rs 20000 from a bank for a period of 1 year. The rate of interest is 10% per annum. Find the simple interest and the total amount he has to pay at the end of a year.

Solution: 

Here, the loan sum = P = Rs 20000

Rate of interest per year = R = 10%

Time (T) = 1 year

Thus, The formula for simple interest for a year,  

SI = (P × R ×T) / 100 

= (20000 × 10 ×1) / 100 

= Rs 2000

Total Amount that Rajesh has to pay to the bank at the end of the year 

Amount = Principal + Simple Interest

= 20000 + 2000 

= Rs 22,000

Question 2: A person borrowed Rs 60,000 for 4 years at the rate of 2.5% per annum. Find the interest accumulated at the end of 4 years.

Solution: 

Given: 

Principal  = Rs 60,000

Rate of interest = 2.5 %

Time  = 4 years

SI = (P × R ×T) / 100 

= ( 60,000 × 2.5 × 4 ) / 100 

= Rs 6000 

Question 3: A person pays Rs 8000 as an amount on the sum of Rs 6000 that he had borrowed for 3 years. What will be the rate of interest?

Solution:

A = Rs 8000

P = Rs 6000

Amount = Principal  + Simple Interest

SI = A – P 

= 8000 – 6000 

= Rs 2000

Time (t) = 3 years

Rate (R) = ?

SI = (P × R ×T) / 100

R = (SI  × 100) /(P× T)

R = (2000  × 100 /(6000 × 3)  

= 11.11 %

Thus, R = 11.11 %

Question 4:  If the principal is Rs 50,000, and the rate of interest is 10% per annum for a period of 4 years. What will be the total amount?

Solution: 

Given: Principal = Rs 50000 

Rate of interest (r) = 10 %

Time period (t) = 4 

 To find total amount, 

Amount = Principal  + Simple Interest

= P + PRT

= P(1 + RT)      

= 50000 {1 + (10/100) × 4}

= 50000 {1+ 40/100}

 = 50000 × 140/100

= 70000

Total amount will be Rs 70000. 

Question 5: If the principal amount is Rs 5000 and the time is 2 years and the simple interest is Rs 4000 what will be the rate of interest?

Solution: 

Given: Principal = Rs 5000 

Time = 2 

Simple interest = 4000

Now, SI = (P × R × T) / 100 

4000 = (5000 × r × 2) /100

4000 = 10000/100 r

(4000 × 100 ) / 10000 = r

r = 400000/10000

r = 40 %

Here rate of interest will be 40 %.

Question 6:  A person has to pay Rs 15000 as an amount on the sum of Rs 9000 that he had borrowed for 3 years. Find the rate of interest over the period?

Solution: 

Given: Amount = Rs 15000

Principal = Rs 7000

Therefore SI = A – P 

= 15000 – 9000

= Rs 6000

Time  = 3 years

R = ?

SI = (P × R × T) / 100

R = (SI × 100) /(P × T)

R = (6000 × 100 / (9000 × 3)  

= 22.22 %

Thus, Rate of interest = 22.22 %