CAT Simple Interest: Relation Among Principal, Time, Rate Percent of Interest Per Annum and Total Interest

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Simple Interest: Relation Among Principal, Time, Rate Percent of Interest Per Annum and Total Interest

Definition: Simple Interest (SI) is the interest earned or paid on the original principal during a specific period.

Formula:

$\mathrm{S I=\frac{P \times R \times T}{100}}$

Where,

P = Principal (initial amount)

R = Rate of interest per annum (in %)

T = Time period (usually in years)

Tip 1: Always make sure your time and rate units match. If the rate is given per annum, your time should also be in years.

Foundation Building Questions:

Question: A sum of ₹4000 is lent out at simple interest for 2 years at 5% per annum. Find the interest earned at the end of 2 years.

Solution:

Using the formula:

$\begin{aligned} & \mathrm{S I=\frac{P \times R \times T}{100}} \\ &\mathrm{ S I=\frac{4000 \times 5 \times 2}{100}} \\ & \mathrm{S I=400} \end{aligned}$

So, the interest earned at the end of 2 years is ₹400.

Tip 2: In questions where you're asked to find the time or rate, rearrange the SI formula to isolate the variable you need to find. For instance, if you need to find time, the formula becomes:

$\mathrm{T=\frac{100 \times S I}{P \times R}}$

Tip 3: If you're given SI for a certain period and asked about another period, remember that SI remains proportional to time. For instance, if SI for 2 years is ₹200, then SI for 3 years would be ₹300 (assuming the rate and principal remain constant).

Solved Example:

Question: An amount of ₹5000 is lent out at a simple interest rate of 3% per annum. How much time will it take for the interest to amount to ₹450?

Solution:

Using the formula:

$\begin{aligned} & \mathrm{T=\frac{100 \times S I}{P \times R}} \\ & \mathrm{ T=\frac{100 \times 450}{5000 \times 3} }\\ & \mathrm{~T}=3 \end{aligned}$

So, it will take 3 years for the interest to amount to ₹450.

Tip 4: For quick calculations, familiarise yourself with common percentages and their decimal equivalents. For instance, 5% is 0.05, and 7% is 0.07. This can help you calculate SI faster.

Remember, practice makes perfect. The more questions you solve related to SI, the quicker and more accurate you'll become.

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