# A man borrowed some money and invested it at compound interest compounded annually. If at the end of 2 years and 3 years, he received the interest of

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A man borrowed some money and invested it at compound interest compounded annually. If at the end of 2 years and 3 years, he received the interest of Rs. 15300 and Rs. 16830 respectively, then find the rate percent per annum at which the sum was invested. Also find the value of compound interest on Rs. 40000 for 1 year.
1. 10% p. a., Rs. 4000
2. Rs. 4000, 10% p. a.
3. Rs. 4400, 20% p. a.
4. 20% p. a., Rs. 4400

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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.