Given: Interest received after 2 years = Rs. 15300 Interest received after 3 years = Rs. 16830 Sum invested on compound interest = Rs. 40000 Concept Used: When a sum is compounded half yearly, its rate percent gets halved and time gets doubled. Formula Used: r% = ((C.I.3 – C.I.2)/C.I.2) × 100 When a sum is compounded half yearly, C.I. = P × (1 + (r/2)/100)2T – 1) where r% → rate percent per annum at which the sum was invested. C.I.2 and C.I.3 → Compound interests after 2 and 3 years respectively. C.I. → Compound Interest, Principal → P, Time period → T. Calculations: Let compound interest after 2 and 3 years be C.I.2 and C.I.3 respectively. r% = ((C.I.3 – C.I.2)/C.I.2) × 100 ⇒ r% = ((16830 – 15300)/15300) × 100 ⇒ r% = (1530/15300) × 100 ⇒ r% = 10% C.I. = P × (1 + (r/2)/100)2T – 1) ⇒ C.I. = Rs. 40000 × (1 + (10/2)/100)2 × 1 – 1) ⇒ C.I. = Rs. 4100 ∴ The rate percent at which the sum was invested is 10% per annum compound interest received when Rs. 40000 are compounded half yearly for 1 year is Rs. 4100.