Ayush invested Rs.75000 in a scheme offering R%p.a. SI for 5 years and Rs.50000 in another scheme offering 12%p.a. CI compounding annually for 2 years. If difference in 2nd year CI and 2nd year SI is Rs.2220, then find value of R%.

Options

A. 0.04
B. 0.08
C. 0.06
D. 0.02

Answer

To solve the problem step by step, let's break it down:

### Step 1: Calculate the Compound Interest (CI) for the second year
We know that Ayush invested Rs. 50,000 at a rate of 12% per annum compounded annually for 2 years. The formula for compound interest is:

\[ A = P(1 + r)^n \]

Where:
- \(A\) = the amount of money accumulated after n years, including interest.
- \(P\) = principal amount (the initial amount of money).
- \(r\) = annual interest rate (decimal).
- \(n\) = number of years the money is invested or borrowed.

For the second year, we need to find the CI for the second year, which is calculated as:

\[ \text{CI for 2nd year} = A_2 - A_1 \]

Where:
- \(A_2\) is the amount after 2 years.
- \(A_1\) is the amount after 1 year.

Calculating \(A_1\) (after 1 year):
\[ A_1 = 50000 \times (1 + 0.12) = 50000 \times 1.12 = 56000 \]

Calculating \(A_2\) (after 2 years):
\[ A_2 = 50000 \times (1 + 0.12)^2 = 50000 \times 1.2544 = 62720 \]

Now, we can find the CI for the second year:
\[ \text{CI for 2nd year} = A_2 - A_1 = 62720 - 56000 = 6720 \]

### Step 2: Calculate the Simple Interest (SI) for the second year
The formula for simple interest is:

\[ SI = \frac{P \times R \times T}{100} \]

Where:
- \(P\) = principal amount.
- \(R\) = rate of interest.
- \(T\) = time in years.

For the second year, the SI can be calculated as:
\[ SI = \frac{75000 \times R \times 1}{100} = \frac{75000R}{100} = 750R \]

### Step 3: Set up the equation using the difference
According to the problem, the difference between the CI for the second year and the SI for the second year is Rs. 2220. Therefore, we can set up the equation:

\[ 6720 - 750R = 2220 \]

### Step 4: Solve for R
Now, let's solve for \(R\):
\[ 6720 - 2220 = 750R \]
\[ 4500 = 750R \]
\[ R = \frac{4500}{750} = 6 \]

### Conclusion
Thus, the value of \(R\) is 6%.