LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

SIMPLE INTEREST - PROBLEM & SOLUTION

**PROBLEM & SOLUTION (SIMPLE INTEREST) -**

**Example.1) John borrowed $2000 from a friend at an annual simple interest rate of 8%. He plans to repay the loan in 3 years. Calculate the total amount John will have to repay, including both the principal and the interest.**

**Ans.) Given:**

**Principal (P) = $2000****Rate (R) = 8% = 0.08 (as a decimal)****Time (T) = 3 years**

**Using the formula for simple interest:-**

** Simple Interest (SI) = Principal (P) × Rate (R) × Time (T)**

**Substitute the values:
SI = $2000 × 0.08 × 3 = $480**

** OR**

** 8**

** SI = $2000 X ------- X 3 = $480 **

** 100**

**Now, to calculate the total amount to be repaid:-**

** Total Amount = Principal + Simple Interest
Total Amount **

** = $2000 + $480 = $2480**

**Total Amount = $2480**

**Therefore, John will have to repay a total amount of $2480, including both the principal and the interest, after 3 years.**

**In this example, the interest earned is $480 over 3 years, which is 8% of the initial $2000 borrowed. This demonstrates how simple interest is calculated and how it contributes to the total repayment amount. (Ans.)**

**Example.2) Tom borrowed $500 from a friend for a period of 3 years at an interest rate of 7% per annum. Calculate the amount of simple interest Tom will have to pay and the total amount he will need to repay at the end of the loan term.**

**Ans.) Given:**

**Principal (P) = $500****Rate (R) = 7% per annum (0.07 as a decimal)****Time (T) = 3 years**

__Step 1:-__ Calculate the simple interest using the formula:-

**Simple Interest (SI) = Principal × Rate × Time**

**SI = $500 × 0.07 × 3 = $105**

** OR**

** 7**

** = $500 X ------ X 3 = $105**

** 100**

__Step 2:-__ Calculate the total amount to be repaid:-

** Total Amount = Principal + Simple Interest
Total Amount **

** = $500 + $105 = $605**

**Answer:
Tom will have to pay $105 as simple interest, and the total amount he needs to repay at the end of the loan term is $605.**

**In this example, the simple interest is calculated as $105, which is 7% of the initial principal amount of $500 for a duration of 3 years. The total amount repaid includes both the principal and the interest, resulting in a final payment of $605. (Ans.)**

**Example.3) John borrowed $2000 from a friend at an interest rate of 8% per year. He needs to repay the loan in 3 years. Calculate the total amount John will have to repay, including the simple interest.**

**Ans.) Given values:
**

**Principal (P) = $2000
**

**Rate (R) = 15% per year (0.15 as a decimal)
**

**Time (T) = 5 years**

**Using the formula for simple interest:-**

**Simple Interest (SI) = P × R × T**

**Calculate the simple interest:
SI = $2000 × 0.15 × 5 = $1500**

** 15**

**Or, S.I = $2000 × --------- × 5 = $1500**

** 100**

**Now, to find the total amount John will have to repay:-**

**
Total Amount = Principal + Simple Interest
Total Amount **

** = $2000 + $1500 = $3500**

**So, John will have to repay a total amount of $3500, which includes the principal of $2000 and the simple interest of $1500, over the course of 5 years at an 15% interest rate. (Ans.)**

**Example.4) Sarah borrowed $4000 from a friend for a period of 10 years at an annual interest rate of 12%. Calculate the total amount of interest she will have to repay at the end of the loan term.**

**Ans.) Given values:**

**Principal (P) = $4000****Rate (R) = 12% = 0.12 (decimal)****Time (T) = 10 years**

**Using the formula for simple interest:****Simple Interest (SI) = Principal (P) × Rate (R) × Time (T)**

**Substitute the values:
SI = $4000 × 0.12 × 10 = $4800**

** OR**

** 12**

** SI = $4000 X -------- X 10 = $4800**

** 100**

**So, Sarah will have to repay a total of $480 in interest at the end of the 10-years loan term.**

**To find the total amount she needs to repay (principal + interest):
**

**Total Amount = Principal + Simple Interest
Total Amount **

** = $4000 + $4800 = $8800**

**Therefore, the total amount Sarah needs to repay at the end of the loan term is $8800, which includes the initial $4000 principal and $4800 in interest. (Ans.)**

**In this example, the problem involved calculating the simple interest and the total amount to be repaid based on the given principal, interest rate, and time period. This is a basic scenario, but it showcases how simple interest works in real-life situations.**