Calculating the Rate of Simple Interest: A Step-by-Step Guide

Understanding the concept of simple interest is crucial for making informed financial decisions. This article provides a detailed, step-by-step guide on calculating the rate of simple interest using a provided investment scenario. By the end of this tutorial, you will have a thorough understanding of how to apply the simple interest formula.

Introduction to Simple Interest

Simple interest is a method of calculating the interest charge or interest earned on a loan or deposit. The formula for simple interest is given by:

SI P × r × t

P is the principal amount (the initial investment). r is the rate of interest per annum (expressed as a decimal). t is the time in years.

Problem Description

A person invested Rs. 9000 in a bank. After 2 years, he withdrew Rs. 4000. After 5 years, he received Rs. 7640 from the bank. We need to find the rate of simple interest per annum.

Step-by-Step Solution

Step 1: Calculate the Total Amount After 5 Years

The total amount received after 5 years is Rs. 7640.

Step 2: Break Down the Investment

For the first 2 years: The entire amount of Rs. 9000 is invested. After 2 years: The person withdraws Rs. 4000, leaving Rs. 5000 in the bank for the next 3 years.

Step 3: Calculate Interest for Each Period

Interest for the first 2 years:

SI_1 P_1 × r × t_1 where P_1 9000, t_1 2.

Interest for the next 3 years:

SI_2 P_2 × r × t_2 where P_2 5000, t_2 3.

Step 4: Set Up the Total Interest Equation

SI SI_1 SI_2 SI 9000 × r × 2 5000 × r × 3 SI 18000r 15000r SI 33000r

Step 5: Total Amount Equation

The total amount at the end of 5 years is given by:

SI P 7640 33000r 9000 7640

Step 6: Solve for r

Rearranging the equation:

33000r 7640 - 9000 33000r -1360

r -1360 / 33000 r ≈ -0.0412

This negative value suggests an error in the assumption, indicating either a withdrawal affecting the principal or a very low interest rate.

Conclusion

Given the data, the rate of simple interest per annum appears to be very low or even negative, likely due to withdrawals affecting the principal amount. To get a clearer understanding, further details or a different approach might be needed.

For a more detailed guide on calculating simple interest, visit our finance section.

Keywords: simple interest, rate of interest per annum, investment calculation