Question: A money-lender borrows money at 5% per annum and pays interest at the end of the year. He lends it at 8% per annum compound interest compounded half-yearly and receives the interest at the end of the year. Thus, he gains Rs. 118.50 in a year. The amount of money he borrows is
Options:
A) Rs. 3450
B) Rs. 3600
C) Rs. 3750
D) Rs. 3900
Show Answer
Answer:
Correct Answer: C
Solution:
- Let the money borrowed be Rs. x.
Interest paid by the money lenders $ =Rs\text{. }( \frac{x\times 1\times 5}{100} )=\frac{x}{20} $
Interest received by the money lender
$ =[ x\times {{( 1+\frac{8/2}{100} )}^{2\times 1}}-x ] $
$ =[ x\times {{( 1+\frac{4}{100} )}^{2}}-x ] $
$ =[ x\times \frac{26}{25}\times \frac{26}{25}-x ]=Rs\text{. }[ x\times ( \frac{676}{625}-1 ) ] $
$ =Rs\text{. }[ x\times ( \frac{51}{625} ) ]\vec{=}Rs\text{. }\frac{51x}{625} $
Now, $ ( \frac{51x}{625}-\frac{x}{20} )=118.50 $
$ \Rightarrow $ $ \frac{204x-125x}{625\times 4}=118.50 $
$ \Rightarrow $ $ \frac{79x}{625\times 4}=118.50 $
$ \Rightarrow $ $ x=( \frac{118.50\times 625\times 4}{79} )=3750 $
BETA
