Question : A certain amount of money was lent for 1 year 9 months at a rate of 10% per annum compounded annually. If the compound interest is INR 1,460, find the amount of money lent.
Option 1: INR 8,200
Option 2: INR 7,500
Option 3: INR 6,000
Option 4: INR 8,000
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Correct Answer: INR 8,000
Solution :
Let the money lent be INR $P$.
Rate of interest, $R$ = 10% per annum
Time, $t$ = 1 year 9 months
Compound interest = INR 1,460
$10\% \; \text {of} \;P + \frac{P\times 10\times 9}{100\times 12} + 10\% \; \text {of} \frac{ \;P\times 10\times 9}{100\times 12}=1460$
⇒ $0.1P + 0.075P+0.0075P=1460$
⇒ $0.1825P = 1460$
⇒ $P =\frac{1460}{0.1825}=8000$
Hence, the correct answer is INR 8000.
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