If ₹360 is the interest earned over 2 years at a 6% rate per annum, what was the initial amount she invested?

Understand the Problem

The question asks how to calculate the initial amount invested, given that a person earns ₹360 as interest over 2 years at a rate of 6% per annum. This involves applying the formula for simple interest to derive the principal amount.

Answer

The initial amount she invested is ₹3000.

Steps to Solve

Identify the formula for simple interest

The formula for calculating simple interest (SI) is given by:

$$ SI = \frac{P \cdot R \cdot T}{100} $$

where:

( P ) = principal amount (initial investment)
( R ) = rate of interest (in %)
( T ) = time (in years)

Substitute known values into the formula

We know:

( SI = 360 ) (interest earned)
( R = 6% ) (rate of interest)
( T = 2 ) (years)

Replace these values in the formula:

$$ 360 = \frac{P \cdot 6 \cdot 2}{100} $$

Simplify the equation to solve for ( P )

Rearranging the equation yields:

$$ 360 = \frac{12P}{100} $$

Multiply both sides by 100 to eliminate the fraction:

$$ 36000 = 12P $$

Solve for ( P )

To find ( P ), divide both sides by 12:

$$ P = \frac{36000}{12} $$

Calculating this gives:

$$ P = 3000 $$

The initial amount she invested is ₹3000.

More Information

This calculation illustrates the concept of simple interest, where the interest earned depends directly on the principal amount, the rate of interest, and the time. Understanding this relationship is crucial for managing personal finances effectively.

Tips

Forgetting to convert the percentage into a decimal or to use it directly in the formula.
Misunderstanding the time period (ensuring it’s in years).
Failing to rearrange the formula correctly to isolate ( P ).

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