Question

What is the time period lor which Rs. 8000 amounts to Rs. 12000 at \(20 \%\) p.a. of simple interest? (a) 4 years (b) \(2.5\) years (c) \(3.25\) years (d) 6 years

Short answer

Answer: 2.5 years

Step-by-step solution

Identify the given values

In this problem, we have the following values: - Principal amount (P): Rs. 8000 - Final amount: Rs. 12000 - Interest rate (R): 20% per annum

Calculate the interest amount

As we have the final amount and the principal amount, we can calculate the interest amount by subtracting the principal amount from the final amount: $$I = \text{Final amount} - \text{Principal}$$ $$I = 12000 - 8000 $$ $$I = 4000$$

Convert the interest rate to the decimal form

Convert the interest rate from percentage to decimal by dividing it by 100: $$R = \frac{20}{100} = 0.2$$

Substitute the given values in the simple interest formula and solve for T

Now, we can plug these values into the simple interest formula \(I = P × R × T\) and solve for the time period (T): $$4000 = 8000 × 0.2 × T$$ To find \(T\), we'll first divide both sides of the equation by (8000 × 0.2): $$T = \frac{4000}{8000 × 0.2}$$ Now, calculate the value of T: $$T = \frac{4000}{1600}$$ $$T = 2.5$$ Thus, the time period for which Rs.8000 amounts to Rs.12000 at 20% p.a. of simple interest is \(2.5\) years. The correct answer is (b) \(2.5\) years.

Key concepts

Principal Amount

The principal amount is the initial sum of money that you invest or lend. In the given exercise, it is the starting amount on which you want to earn interest. Think of it as the base from which all interest calculations begin.
For instance:

• In our exercise, the principal amount is Rs. 8000.

This means that the transaction starts with Rs. 8000 as the base amount. When you calculate interest, its effects multiply this base. Understanding the principal amount is crucial because it directly affects the amount of interest you earn or owe.

Interest Rate

The interest rate is the percentage at which the principal amount will gain interest over a specified period, usually annually. It shows how profitable or costly the transaction can be.
In our exercise, the interest rate is

• 20% per annum (p.a.).

"Per annum" means that the percentage applies for one year. To use the interest rate in calculations, it's often converted to a decimal format. For 20%, you divide by 100, resulting in 0.2. This conversion is essential for using the established formulas for calculations.
Higher interest rates generally mean more interest will be earned on the principal amount, but it's important to balance this with the time period to assess overall returns.

Time Period

The time period is the duration for which the principal amount is invested or borrowed, during which the interest is applied. It plays a crucial role in determining the total interest earned or paid.
In this specific scenario, the calculated time period

• is 2.5 years.

This means that the principal amount is subject to the 20% interest rate annually for two and a half years. The time period helps us understand how long the investment grows or how long you'll owe interest on a loan.
Understanding the time period is especially important in planning and financial forecasting, as it can significantly impact the total amount of interest accrued.

Interest Calculation

Interest calculation involves computing the amount of interest accrued over a certain period, using the simple interest formula. The formula typically used is: \[ I = P \times R \times T \]Here, \(I\) is the interest, \(P\) is the principal amount, \(R\) is the rate of interest (as a decimal), and \(T\) is the time period (in years).
In our exercise:

• The interest calculated is Rs. 4000.

By knowing the final amount and subtracting the principal, you find this interest value. Substituting the known values in the formula allows you to either find the missing time period, rate, or directly determine the interest. It's a flexible formula that's part and parcel with any basic financial literacy toolkit.
Understanding how to perform this calculation is crucial, as it enables efficient financial planning and helps individuals make informed decisions about investments or loans.