What will Rs.1500 amount to in three years if it is invested in 20% p.a.…
2024
What will Rs.1500 amount to in three years if it is invested in 20% p.a. compound interest, interest being compounded annually?
Answer: B. Rs. 2592 — Concept: Compound interest grows the principal by a fixed percentage each period, and each new period's interest is calculated on the previous period's…
- A.
Rs. 2400
- B.
Rs. 2592
- C.
Rs. 2678
- D.
Rs. 2540
Attempted by 2 students.
Show answer & explanation
Correct answer: B
Concept: Compound interest grows the principal by a fixed percentage each period, and each new period's interest is calculated on the previous period's already-grown amount. The amount after T years at rate R% p.a., compounded annually, is A = P(1 + R/100)T.
Application:
Identify the values: Principal P = Rs. 1500, Rate R = 20% p.a., Time T = 3 years.
Substitute into A = P(1 + R/100)T to get A = 1500 × (1 + 20/100)3 = 1500 × (1.2)3.
Compute the growth factor: 1.2 × 1.2 = 1.44, and 1.44 × 1.2 = 1.728.
Multiply: A = 1500 × 1.728 = Rs. 2592.
Cross-check: Compute year by year on the running balance — Year 1: 1500 + 20% of 1500 = 1800; Year 2: 1800 + 20% of 1800 = 2160; Year 3: 2160 + 20% of 2160 = 2592. This matches the formula result, confirming Rs. 2592 is correct.