Correct Answer - Option 1 : 10% p. a., Rs. 4000

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)/100)T – 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)/100)T – 1)

⇒ C.I. = Rs. 40000 × (1 + (10/100)1 – 1)

⇒ C.I. = Rs. 4000

∴ The rate percent at which the sum was invested is 10% per annum compound interest received when Rs. 40000 are compounded for 1 year is Rs. 4000.