Question

Mr. Dua invested money in two schemes, A and B offering compound interest @ 8 p.c.p.a and 12 p.c.p.a respectively. If the total amount of interest accrued through two schemes together in two years was Rs.\ 4538.00 and the total amount invested was Rs.\ 20,000, what was the amount invested in Scheme A?

• A. Rs.\ 6000
• B. Rs.\ 6250
• C. Rs.\ 6500
• D. Rs.\ 16000
• E. Rs.\ 16500

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The problem requires us to find the specific principal amount invested in Scheme A out of a total investment of Rs. 20,000.
We are given that Scheme A offers an 8% compound interest per annum, while Scheme B offers a 12% compound interest per annum.
The total compound interest earned from both investments combined at the end of two years is given as Rs. 4538.00.
Step 2: Key Formula or Approach:
For compound interest, the effective rate of interest for two years at a rate of $R$% per annum can be calculated using the successive percentage formula: $\text{Effective Rate} = R + R + \frac{R \times R}{100}$%.
Alternatively, we can use the standard compound interest formula, but the effective rate is much faster.
We will set up a linear equation by assuming the amount invested in Scheme A is $x$.
Step 3: Detailed Explanation:

Let the amount invested by Mr. Dua in Scheme A be denoted as Rs. $x$.

Since the total investment is Rs. 20,000, the amount invested in Scheme B must be Rs. $(20000 - x)$.

First, we calculate the effective compound interest rate for Scheme A over the two-year period.

Using the formula, the effective rate for Scheme A is $8 + 8 + \frac{8 \times 8}{100} = 16.64$%.

Next, we calculate the effective compound interest rate for Scheme B over the two-year period.

The effective rate for Scheme B is $12 + 12 + \frac{12 \times 12}{100} = 25.44$%.

Now, we can express the total compound interest earned as the sum of the interests from both schemes.

This gives us the algebraic equation: \[ 0.1664x + 0.2544(20000 - x) = 4538 \]

We expand the terms in the equation to simplify it.

\[ 0.1664x + 5088 - 0.2544x = 4538 \]

Next, we group the variable terms on one side and the constant terms on the other side.

\[ 5088 - 4538 = 0.2544x - 0.1664x \]

Subtracting the values, we obtain: \[ 550 = 0.088x \]

To isolate $x$, we divide both sides of the equation by 0.088.

\[ x = \frac{550}{0.088} \]

To make the division easier, we multiply the numerator and the denominator by 1000.

\[ x = \frac{550000}{88} \]

Dividing 550000 by 88 yields exactly 6250.

Thus, the amount invested in Scheme A is Rs. 6250.

Step 4: Final Answer:
The total amount invested in Scheme A is Rs. 6250.