Find the compound interest when sum of ₹50,000 is invested for 3 years at 12% per annum compounded annually

Question

Accepted Answer

The correct option is 1:
To solve this problem, we need to understand the concept of compound interest and its formula. Compound interest is the interest calculated on the initial principal and also on the accumulated interest from previous periods on a deposit or loan.

The formula for the Amount (A) with compound interest is:
$$A = P \left(1 + \frac{R}{100}\right)^n$$
Where:  - $P$ = Principal amount
  - $R$ = Annual interest rate (as a percentage)
  - $n$ = Number of years
  - $A$ = Amount after $n$ yearsThe compound interest (CI) is then calculated as:
$$CI = A - P$$

Given values are:  - Principal amount ($P$) = ₹50,000
  - Annual interest rate ($R$) = 12%
  - Number of years ($n$) = 3 yearsStep-by-step calculation:1.  Substitute the given values into the amount formula:
    $$A = 50000 \left(1 + \frac{12}{100}\right)^3$$
    $$A = 50000 \left(1 + 0.12\right)^3$$
    $$A = 50000 \left(1.12\right)^3$$

2.  Calculate $(1.12)^3$:
    $$1.12 \times 1.12 = 1.2544$$
    $$1.2544 \times 1.12 = 1.404928$$

3.  Multiply by the principal amount to find the total amount:
    $$A = 50000 \times 1.404928$$
    $$A = 70246.40$$

4.  Calculate the compound interest (CI):
    $$CI = A - P$$
    $$CI = 70246.40 - 50000$$
    $$CI = 20246.40$$Thus, the compound interest is ₹20,246.40.

The incorrect option is 2:
₹80,000 is incorrect because it is significantly higher than the actual amount and does not reflect a correct calculation of compound interest. This value might represent a rough estimation without proper calculation or a calculation error.

The incorrect option is 3:
₹70,000 is incorrect. This value is close to the total amount (Principal + Compound Interest), but it is not the compound interest itself. It might be a rounded figure of the total amount or a calculation mistake.

The incorrect option is 4:
₹70,246.40 is incorrect. This value represents the total Amount ($A$), which is the principal plus the compound interest. The question asks specifically for the "compound interest", not the final amount.