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Q.

Rahul took a loan of Rs.1024000 from a bank for one year. If the bank charges interest of 5% per annum, compounded for 6 months, then the interest paid by Rahul is Rs. ____.


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Detailed Solution

Rahul took a loan of Rs.1024000 from a bank for one year. If the bank charges interest of 5% per annum, compounded for 6 months, then the interest paid by Rahul is Rs.51840.
We have given,
Principal (P) = Rs.1024000.
Rate (R) = 5% p.a.
Time period (t) = 1 year.
We know that the formula for compound interest if the interest is compounded for 6 months is,
C.I.=P 1+ R 200 2t −P  
And,
Total Amount = Principal Amount + C.I.
⇒Total amount=P+ P 1+ R 200 2t −P ⇒Total amount=P 1+ R 200 2t  
⇒Total amount=1024000 1+ 5 200 2×1 ⇒Total amount=1024000 41 40 2 ⇒Total amount=640×41×41 ⇒Total amount=Rs.1075840  
Therefore, C.I. = Total Amount - Principal Amount
⇒C.I.=Rs.1075840 −Rs.1024000 =Rs.51840   Therefore, the interest paid by Rahul is Rs.51840.
 
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