The compound interest earned by Sunil on a certain amount at the end of two years at the rate of 8% p.a. was Rs.2828.80. Find the total amount that Sunil got back at the end of two years in the form of principal plus interest earned ?

Options

A. A. 19328.80
B. B. 9828.80
C. C. 8000
D. D. 11828.80

Answer

To find the total amount that Sunil got back at the end of two years, we first need to determine the principal amount using the compound interest formula.

### Step-by-Step Solution:

1. **Understand the Compound Interest Formula**:
The formula for compound interest (CI) is given by:
\[ CI = P \left(1 + \frac{r}{100}\right)^n - P \]
where:
- \( CI \) = Compound Interest
- \( P \) = Principal amount
- \( r \) = Rate of interest per annum
- \( n \) = Number of years

2. **Rearranging the Formula**:
We can rearrange the formula to find the principal \( P \):
\[ CI = P \left( \left(1 + \frac{r}{100}\right)^n - 1 \right) \]
Thus, we can express \( P \) as:
\[ P = \frac{CI}{\left(1 + \frac{r}{100}\right)^n - 1} \]

3. **Substituting the Known Values**:
From the question:
- \( CI = 2828.80 \)
- \( r = 8\% \)
- \( n = 2 \)

Now substitute these values into the formula:
\[ P = \frac{2828.80}{\left(1 + \frac{8}{100}\right)^2 - 1} \]

4. **Calculating the Compound Factor**:
First, calculate \( \left(1 + \frac{8}{100}\right)^2 \):
\[ 1 + \frac{8}{100} = 1.08 \]
Now calculate \( (1.08)^2 \):
\[ (1.08)^2 = 1.1664 \]
Thus,
\[ (1.08)^2 - 1 = 1.1664 - 1 = 0.1664 \]

5. **Calculating the Principal**:
Now substitute this back into the equation for \( P \):
\[ P = \frac{2828.80}{0.1664} \]
Calculating this gives:
\[ P \approx 17000 \]

6. **Finding the Total Amount**:
The total amount \( A \) at the end of two years is given by:
\[ A = P + CI \]
Substitute the values:
\[ A = 17000 + 2828.80 = 19828.80 \]

### Final Answer:
The total amount that Sunil got back at the end of two years is Rs. 19828.80.