Investment Calculation: Scheme A vs Scheme B

Let the amount invested in Scheme A be denoted by $P_A$ and the amount invested in Scheme B be denoted by $P_B$. The total investment is ₹55,800.

We are given:

• Total Investment: $P_{Total} = P_A + P_B = ₹55,800$
• Scheme A: Compound Interest (CI), Rate $R_A = 20\%$ p.a., Time $T_A = 2$ years.
• Scheme B: Simple Interest (SI), Rate $R_B = 20\%$ p.a., Time $T_B = 4$ years.
• Interest earned from both schemes is equal: $CI_A = SI_B$.

Scheme A: Compound Interest Calculation

The formula for Compound Interest is $CI = P \times [(1 + R/100)^T - 1]$.

For Scheme A:

$CI_A = P_A \times [(1 + 20/100)^2 - 1]$

$CI_A = P_A \times [(1.2)^2 - 1]$

$CI_A = P_A \times [1.44 - 1]$

$CI_A = P_A \times 0.44$

Scheme B: Simple Interest Calculation

The formula for Simple Interest is $SI = (P \times R \times T) / 100$.

For Scheme B:

$SI_B = (P_B \times 20 \times 4) / 100$

$SI_B = (P_B \times 80) / 100$

$SI_B = P_B \times 0.80$

Equating Interests and Solving for $P_A$

Given that $CI_A = SI_B$:

$P_A \times 0.44 = P_B \times 0.80$

Since $P_B = 55800 - P_A$, substitute this into the equation:

$P_A \times 0.44 = (55800 - P_A) \times 0.80$

$0.44 P_A = 55800 \times 0.80 - 0.80 P_A$

$0.44 P_A = 44640 - 0.80 P_A$

Combine the $P_A$ terms:

$0.44 P_A + 0.80 P_A = 44640$

$1.24 P_A = 44640$

Solve for $P_A$:

$P_A = 44640 / 1.24$

$P_A = 36000$

Conclusion

The amount invested in Scheme A is ₹36,000.