In what time will rupees 8000 amount to 8820 at 10% per annum interest compounded half yearly?

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Find the time period if Rs 8,000 becomes Rs 9,261 at 5 % p.a. compounded annually.

Question

A

2.5 years

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B

3 years

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C

2 years

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D

4 years

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Solution

The correct option is B3 years

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The compound interest and the amount obtained, on a certain sum of money are ₨. 820 and ₨. 8,820 respectively after 2 years. If the rate of interest compounded yearly, then the rate of interest is:

1. 8%
2. 7%
3. 6%
4. 5%

Answer (Detailed Solution Below)

Option 4 : 5%

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January Month Current Affair (1st Jan - 15th Jan)

30 Questions 30 Marks 30 Mins

Given:

CI of 2 years = Rs. 820

Amount = Rs. 8820

Time = 2 years

Formula:

A = P (1 + r/100)t 

Calculation:

Amount = Rs. 8820 

CI = Rs. 820

Principal = Rs. 8820 - Rs. 820 = Rs. 8000

According to the formula

8820 = 8000 (1 + r/100)2

⇒ (1 + r/100)2 = 8820/8000

⇒ (1 + r/100)2 = 441/400

⇒ (1 + r/100) = √441/400

⇒ (1 + r/100) = 21/20

⇒ r/100 = 21/20 - 1

⇒ r/100 = 1/20

⇒ r = 5%

∴ The rate of interest is 5%.

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