A sum invested for 3 yr compounded at 5% , 10% and 20% respectively. In 3yr , if the sum amount to ? 16632, then find the sum

Options

A. ? 11000
B. ? 12000
C. ? 9000
D. ? 15000

Answer

To find the principal sum (P) that, when invested for 3 years at different compound interest rates (5%, 10%, and 20%), amounts to ₹16,632, we can use the formula for compound interest:

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

Where:
- \( A \) is the amount after time \( n \)
- \( P \) is the principal amount (the initial sum)
- \( r \) is the rate of interest per annum
- \( n \) is the number of years

Given that the amount \( A \) is ₹16,632 and \( n \) is 3 years, we will calculate the principal for each interest rate.

### Step 1: Calculate the principal for 5% interest
Using the formula:

\[ 16632 = P \left(1 + \frac{5}{100}\right)^3 \]

Calculating \( \left(1 + \frac{5}{100}\right)^3 \):

\[ \left(1 + 0.05\right)^3 = (1.05)^3 = 1.157625 \]

Now substituting back into the equation:

\[ 16632 = P \times 1.157625 \]

To find \( P \):

\[ P = \frac{16632}{1.157625} \]

Calculating \( P \):

\[ P \approx 14300.00 \]

### Step 2: Calculate the principal for 10% interest
Using the formula:

\[ 16632 = P \left(1 + \frac{10}{100}\right)^3 \]

Calculating \( \left(1 + \frac{10}{100}\right)^3 \):

\[ \left(1 + 0.10\right)^3 = (1.10)^3 = 1.331 \]

Now substituting back into the equation:

\[ 16632 = P \times 1.331 \]

To find \( P \):

\[ P = \frac{16632}{1.331} \]

Calculating \( P \):

\[ P \approx 12499.25 \]

### Step 3: Calculate the principal for 20% interest
Using the formula:

\[ 16632 = P \left(1 + \frac{20}{100}\right)^3 \]

Calculating \( \left(1 + \frac{20}{100}\right)^3 \):

\[ \left(1 + 0.20\right)^3 = (1.20)^3 = 1.728 \]

Now substituting back into the equation:

\[ 16632 = P \times 1.728 \]

To find \( P \):

\[ P = \frac{16632}{1.728} \]

Calculating \( P \):

\[ P \approx 9625.00 \]

### Summary of Results
- For 5% interest: Principal \( P \approx ₹14,300.00 \)
- For 10% interest: Principal \( P \approx ₹12,499.25 \)
- For 20% interest: Principal \( P \approx ₹9,625.00 \)