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Question
Sunil borrows Rs.50,000 at 10% S.I. for 1`(1)/(2)` years. He immediately invests the entire amount for 1`(1)/(2)` years at 10% compounded annually. What is his gain at the end of the stipulated time, when he repays his loan?
Solution
To calculate the S.I. paid by Sunil :
P = Rs.50000, R = 10% and T = 1`(1)/(2)` years = `(3)/(2)` years
∴ S.I. = Rs.`(50000 xx 10 xx 3)/(100 xx 2)`
= Rs.7500
To calculate the C.I. earned by Sunil :
For 1st year : P = Rs.50000, R = 10% and T = 1 year
∴ Interest = RS.`(50000 xx 10 xx 1)/(100)`
= Rs.5000
And, amount
= Rs.50000 + Rs.5000
=Rs. 55000
For next half year : P = Rs.55000, R = 10% and T = `(1)/(2)` year
∴ Interest = Rs.`(55000 xx 10 xx 1)/(100 xx 2)`
= Rs.2750
And, amount
= Rs. 55000 + Rs.2750
= Rs.7750
∴ Total C.I. earned
= Rs.55750 + Rs.2750
= Rs.57750
⇒ Sunil's gain in 1`(1)/(2)` year
= C.I. earned - S.I. paid
= Rs.250.
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