This is a standard Simple Interest (SI) and Compound Interest (CI) problem from Class 8 Maths. Preeti invests Rs 50,000 at 8% per annum. We calculate the interest and amount for different time periods using both Simple Interest and Compound Interest formulas.
P = Rs 50,000; R = 8% per annum.
SI for 1 year = Rs 4,000; for 2 years = Rs 8,000; for 3 years = Rs 12,000.
CI for 2 years = Rs 8,320; for 3 years = Rs 12,985.60.
Amount (CI, 2 years) = Rs 58,320; Amount (CI, 3 years) = Rs 62,985.60.
Difference CI – SI for 2 years = Rs 320.
CI > SI for the same P, R and T (when T > 1 year).
Principal (P) = Rs 50,000 Rate of Interest (R) = 8% per annum Time periods: 1 year, 2 years, 3 years
Formulas: Simple Interest (SI) = (P × R × T) / 100 Amount (A) = P + SI
Compound Interest (CI): A = P(1 + R/100)ⁿ CI = A – P
For T = 1 year: SI = (50000 × 8 × 1) / 100 = Rs 4,000 Amount = 50,000 + 4,000 = Rs 54,000
For T = 2 years: SI = (50000 × 8 × 2) / 100 = Rs 8,000 Amount = 50,000 + 8,000 = Rs 58,000
For T = 3 years: SI = (50000 × 8 × 3) / 100 = Rs 12,000 Amount = 50,000 + 12,000 = Rs 62,000
For T = 1 year: A = 50000 × (1 + 8/100)¹ = 50000 × 1.08 = Rs 54,000 CI = 54,000 – 50,000 = Rs 4,000 (Same as SI for 1 year)
For T = 2 years: A = 50000 × (1.08)² = 50000 × 1.1664 = Rs 58,320 CI = 58,320 – 50,000 = Rs 8,320
For T = 3 years: A = 50000 × (1.08)³ = 50000 × 1.259712 = Rs 62,985.60 CI = 62,985.60 – 50,000 = Rs 12,985.60
For T = 2 years: CI – SI = Rs 8,320 – Rs 8,000 = Rs 320
For T = 3 years: CI – SI = Rs 12,985.60 – Rs 12,000 = Rs 985.60
Key insight: Compound Interest is always greater than Simple Interest for the same principal, rate, and time (for T > 1 year). The difference increases as time increases.
SI = (P × R × T) / 100 = (50000 × 8 × 2) / 100 = Rs 8,000. Amount = 50,000 + 8,000 = Rs 58,000.
A = P(1 + R/100)ⁿ = 50000 × (1.08)² = 50000 × 1.1664 = Rs 58,320. CI = 58,320 – 50,000 = Rs 8,320.
A = 50000 × (1 + 8/100)³ = 50000 × (1.08)³ = 50000 × 1.259712 = Rs 62,985.60. Compound Interest = Rs 12,985.60.
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