Rohit decides to invest a certain amount of
money in savings account of a bank that pays
20% compound interest per annum for a
period of two years. What is the sum of money
that Rohit should invest so that he receives
Rs. 200 at the end of first year, and Rs. 400
at the end of second year?

Let the sum of money Rohit invests be denoted as \( P \).

The formula for compound interest is:

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

Where:
- \( A \) is the amount after time \( t \),
- \( P \) is the initial principal,
- \( r \) is the annual interest rate (in this case, 20%),
- \( t \) is the number of years.

We are given two conditions:
1. Rohit should receive Rs. 200 at the end of the first year.
2. Rohit should receive Rs. 400 at the end of the second year.

### Step 1: Equation for the first year

At the end of the first year, the amount \( A_1 \) is:

\[
A_1 = P \left(1 + \frac{20}{100}\right)^1 = P \times 1.2
\]

We know \( A_1 = 200 \). So,

\[
200 = P \times 1.2
\]

Solving for \( P \):

\[
P = \frac{200}{1.2} = \frac{2000}{12} = 166.67 \, \text{Rs.}
\]

### Step 2: Equation for the second year

Now, for the second year, the amount \( A_2 \) is:

\[
A_2 = P \left(1 + \frac{20}{100}\right)^2 = P \times 1.2^2 = P \times 1.44
\]

We know \( A_2 = 400 \). So,

\[
400 = P \times 1.44
\]

Solving for \( P \):

\[
P = \frac{400}{1.44} = \frac{40000}{144} = 277.78 \, \text{Rs.}
\]

### Conclusion

To satisfy both conditions, the initial investment should be **Rs. 277.78**.

Would you like a more detailed breakdown or have any other questions?

Here are 5 related questions you might explore:
1. How does simple interest compare to compound interest over multiple years?
2. What would be Rohit's return if the interest rate were compounded quarterly instead of annually?
3. How would the investment grow if the interest rate was 10% instead of 20%?
4. How do you calculate the compound interest for a period of 5 years?
5. What is the total interest earned in this scenario?

**Tip:** Compound interest grows faster than simple interest because interest is calculated on both the initial principal and the accumulated interest.

Rohit decides to invest a certain amount of money in a savings account of a bank that pays 20% compound interest per annum for a period of two years. What is the sum of money that Rohit should invest so that he receives Rs. 200 at the end of first year, and Rs. 400 at the end of second year?

Discover how to calculate the sum of money Rohit should invest to receive Rs. 200 at the end of the first year and Rs. 400 at the end of the second year with 20% compound interest. This example includes step-by-step explanations of the compound interest formula, suitable for students in Grades 9-10.

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