Calculating Principal Amount in Simple Interest Problems: A Comprehensive Guide

Simple interest is a straightforward method for calculating the interest on a principal amount over a specified period. In this article, we will explore how to determine the principal amount borrowed when given the simple interest, rate of interest, and time period through a series of examples.

Example Problems and Solutions

Problem 1: Ajay's Loan Calculation

Ajay took a loan from a bank at the rate of 6% per annum simple interest. After 3 years, he had to pay Rs. 3600 interest only for the period. What was the principal amount borrowed by him?

To solve this problem, we use the simple interest formula:

$$ Simple Interest (SI) frac{P times R times T}{100} $$

Where:

SI is the simple interest (Rs. 3600).

P is the principal amount (to be determined).

R is the rate of interest per annum (6%).

T is the time in years (3).

Substituting the known values into the formula:

$$ 3600 frac{P times 6 times 3}{100} $$

Now simplifying this equation:

$$ 3600 frac{18P}{100} $$

Multiplying both sides by 100 to eliminate the fraction:

$$ 360000 18P $$

Dividing both sides by 18 to find P:

$$ P frac{360000}{18} Rs. 20000 $$

The principal amount borrowed by Ajay was Rs. 20000.

Problem 2: Another Simple Interest Calculation

The interest (Rs. 2700) is divided by the period (3 years). The interest for 1 year is Rs. 900. If we divide Rs. 900 by the rate of interest (0.06), we get the principal amount.

$$ 900 div 0.06 Rs. 15000 $$

Hence, the principal amount borrowed is Rs. 15000.

Problem 3: Principal Amount Calculation

Let the principal amount borrowed from a bank be Rs. P.

At a rate of interest of 10% and a period of 2 years, the interest is Rs. 3600.

Using the formula:

$$ 3600 P times 2 times 0.10 $$

Solving for P:

$$ P frac{3600}{2 times 0.10} Rs. 18000 $$

The principal amount borrowed was Rs. 18000.

Problem 4: Reverse Calculation Using Simple Interest Formula

The principal amount borrowed can be determined using the formula:

$$ Principal frac{SI times 100}{T times R} $$

Given SI 3600, N 2 years, and R 10%:

$$ Principal frac{3600 times 100}{2 times 10} Rs. 18000 $$

The principal amount borrowed is Rs. 18000.

Problem 5: Additional Interest Calculation

Given that the interest for 4 years is Rs. 6000, the interest for 1 year is Rs. 1500. The principal amount can be calculated as:

$$ Amount frac{1500 times 100}{12} Rs. 12500 $$

The principal amount is Rs. 12500.

Problem 6: Direct Application of Simple Interest Formula

The simple interest formula can be expressed as:

$$ A P times frac{1 times R times T}{100} $$

Given SI 3600, R 10%, and T 2 years:

$$ 3600 P times frac{1 times 10 times 2}{100} $$

Simplifying and solving for P:

$$ P frac{3600 times 100}{1 times 10 times 2} Rs. 18000 $$