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A sum of money is invested at 20% compound interest (compounded annually). It would fetch Rs. 723 more in 2 years if interest is compounded half yearly. The sum is
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- Rs.15,000
- Rs.30,000
- Rs.20,000
- Rs.7,500
Correct Option: B
Let the principal be Rs. P.
When the interest is compounded annually,
C.I. = P | ![]() | ![]() | 1 + | ![]() | T | − 1 | ![]() | |
100 |
C.I. = P | ![]() | ![]() | 1 + | ![]() | 2 | − 1 | ![]() | |
100 |
C.I. = P | ![]() | ![]() | ![]() | 2 | − 1 | ![]() | |
5 |
C.I. = P | ![]() | − 1 | ![]() | |
25 |
C.I. = Rs. | |
25 |
When the interest is compounded half–yearly,
C.I. = P | ![]() | ![]() | 1 + | ![]() | 4 | − 1 | ![]() | |
100 |
C.I. = P | ![]() | ![]() | ![]() | 4 | − 1 | ![]() | |
10 |
C.I. = P | ![]() | − 1 | ![]() | |
10000 |
C.I. = Rs. | |
10000 |
From the question ,
∴ | − | = 723 | ||
10000 | 25 |
⇒ | = 723 | |
10000 |
⇒ | = 723 | |
10000 |
⇒ P = | = Rs. 30000 | |
241 |