A sum fetched a total simple interest of Rs.4016.25 at the rate of 9 p.c.p.a in 5 years. What is the sum?

A sum fetched a total simple interest of Rs.4016.25 at the rate of 9 p.c.p.a in 5 years. What is the sum?

To determine the principal sum that generated a total simple interest of Rs. 4016.25 at an annual interest rate of 9% over 5 years, we can follow a structured approach using the simple interest formula.

Simple Interest (SI): Rs. 4016.25

Rate of Interest (R): 9% per annum

Time (T): 5 years

We will use the simple interest formula to find the principal amount (P):

SI = (P×R×T​)/100

To find the principal amount P, rearrange the simple interest formula:

P = (SI×100​)/RxT

Substitute the values of SI, R, and T into the rearranged formula

P = (4016.25x100)/(9x5)

P = 401625/45

​P = 8925

The principal amount (P) that fetched a total simple interest of Rs. 4016.25 at an interest rate of 9% per annum over 5 years is Rs. 8925.

Concept of Simple Interest

Simple interest is a fundamental concept in finance and mathematics that helps determine the interest earned or paid on a principal amount over a specific period at a fixed rate. It is the interest calculated on the principal amount or initial sum of money, without considering any interest that has been added over time. The formula for calculating simple interest is:

SI = (P×R×T​)/100

where:

• SI is the simple interest
• P is the principal amount
• R is the rate of interest per annum
• T is the time period in years

Key Points

Principal Amount (P):

This is the initial sum of money that is either invested or borrowed. It is the base amount on which interest is calculated.

Rate of Interest (R):

This is the percentage at which interest is calculated on the principal amount annually. It represents the cost of borrowing or the gain from investing money.

Time Period (T):

This refers to the duration for which the money is borrowed or invested. It is usually measured in years.

Interest Calculation:

Simple interest is simple to calculate as it does not compound. It means the interest is calculated only on the principal amount and remains constant throughout the period.

Rules and Considerations

• Simple interest is calculated at a fixed rate, meaning the rate of interest remains unchanged throughout the period.
• Unlike compound interest, simple interest does not compound, so the interest earned or paid each period is based solely on the principal amount.
• The time frame for calculating simple interest is usually in years, but it can also be adjusted for months or days by converting the time period appropriately.
• Ensure that the rate of interest and time period are in the same units (e.g., both in years) to avoid errors in calculation.