What is the sum of money which will become Rs. 201840 at the rate of 16% per annum at compound interest in two years ?

Options

A. Rs. 160000
B. Rs. 150000
C. Rs. 180000
D. Rs. 200000

Answer

To find the sum of money (principal amount) that will become Rs. 201840 at the rate of 16% per annum compounded annually in 2 years, we can use the formula for compound interest:

\[ A = P \left(1 + \frac{r}{100}\right)^n \]

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

Given:
- \( A = 201840 \)
- \( r = 16\% \)
- \( n = 2 \)

### Step 1: Substitute the known values into the formula

We can rearrange the formula to solve for \( P \):

\[ P = \frac{A}{\left(1 + \frac{r}{100}\right)^n} \]

Substituting the values:

\[ P = \frac{201840}{\left(1 + \frac{16}{100}\right)^2} \]

### Step 2: Calculate \( 1 + \frac{r}{100} \)

Calculate \( 1 + \frac{16}{100} \):

\[ 1 + \frac{16}{100} = 1 + 0.16 = 1.16 \]

### Step 3: Raise the result to the power of n

Now raise \( 1.16 \) to the power of \( 2 \):

\[ (1.16)^2 = 1.16 \times 1.16 = 1.3456 \]

### Step 4: Substitute back to find P

Now substitute this back into the equation for \( P \):

\[ P = \frac{201840}{1.3456} \]

### Step 5: Calculate the value of P

Now perform the division:

\[ P = \frac{201840}{1.3456} \approx 149,000 \]

### Conclusion

The sum of money (principal amount) that will become Rs. 201840 at the rate of 16% per annum compounded annually in 2 years is approximately Rs. 149,000.

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