When principal = Rs.S , rate of interest - `2r %` p.a, then a person will get after 3 years at compound interest

Options

A. `Rs.(65r)/(100)`
B. `Rs.S(1+(r)/(100))^3`
C. `Rs.S(1+(r)/(50))^3`
D. `Rs.3S(1+(r)/(50))^3`

Answer

To solve the problem of calculating the amount after 3 years at compound interest, we can follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs. S
- Rate of Interest (R) = 2r% per annum
- Time (T) = 3 years

### Step 2: Convert the rate of interest into decimal form
To use the formula for compound interest, we need to express the rate of interest as a decimal:
\[ R = \frac{2r}{100} \]

### Step 3: Use the compound interest formula
The formula for calculating the amount (A) after time T at compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
Substituting the values we have:
\[ A = S \left(1 + \frac{2r}{100}\right)^3 \]

### Step 4: Simplify the expression
Now we can simplify the expression:
\[ A = S \left(1 + \frac{2r}{100}\right)^3 \]

### Step 5: Final expression
The final amount after 3 years will be:
\[ A = S \left(1 + \frac{2r}{100}\right)^3 \]

### Summary
Thus, the amount after 3 years at compound interest when the principal is Rs. S and the rate of interest is 2r% per annum is:
\[ A = S \left(1 + \frac{2r}{100}\right)^3 \]

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