A certain amount invested at 15% compound interest per annum, compounded annually, becomes ₹4,235 in 2 years. What is 120% of the principal?

Correct Answer: ₹3,840

Step-by-Step Explanation:

Step 1: Understand the given data
- Rate of compound interest (R) = 15% per annum
- Time period (n) = 2 years
- Amount after 2 years (A) = ₹4,235
Let the principal amount be P.

Step 2: Use the Compound Interest Formula
The formula for the total amount A compounded annually is:

$A=P{\left(1+\frac{R}{100}\right)}^n$

Substituting the given values into the formula:

$4235=P{\left(1+\frac{15}{100}\right)}^2$

Step 3: Simplify the equation to find the Principal (P)
Simplify the fraction inside the parentheses:

$1+\frac{15}{100}=1+\frac{3}{20}=\frac{23}{20}$

Now, raise it to the power of 2:

${\left(\frac{23}{20}\right)}^2=\frac{529}{400}$

Substitute this back into the equation:

$4235=P\times \frac{529}{400}$

Solve for P:

$P=\frac{4235\times 400}{529}$

Dividing 4235 by 529 gives 8:

$P=8\times 400=3200$

So, the principal amount (P) is ₹3,200.

Step 4: Calculate 120% of the principal
We need to find 120% of ₹3,200:

$\text{Required Amount}=\frac{120}{100}\times 3200$

$\text{Required Amount}=120\times 32=3840$

Thus, 120% of the principal is ₹3,840.