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Q.


Arif took a loan of Rs. 80,000 from a bank. If the rate of interest is 10% per annum, find the difference in amounts he would be paying after 1 1 2  years if the interest is compounded annually.

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a

Rs 92100

b

Rs 92200

c

Rs 92300

d

Rs 92400 

answer is D.

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Detailed Solution

Given that,
Principal (P) = Rs 80000,
Rate (R) = 10% per annum compounded half yearly,
Number of years (n) = 1 1 2   years
We know that,
Amount=principal 1+ R 100 Time  
Then,
Amount=principal 1+ R 100 Time ⇒Amount=80000 1+ 10 100 1 ⇒Amount=80000 100+10 100 1 ⇒Amount=80000 110 100 1 ⇒Amount=80000× 11 10 ⇒Amount=Rs.88000  
Calculate the interest for 1 year,
Interest = Amount – Principal
⇒  Interest = (88000 – 80000)
⇒  Interest = 8000
Interest for 1 year = Rs 8000.
Simple interest for next 1 2   year
P= amount in previous year = 88000,
R= 10%,
Time= 1 2  year
We know that,
SI= PRT 100 ⇒SI= 88000×10× 1 2 100 ⇒SI=Rs.4400  
Now, calculate interest after 3 2   years.
Interest after 1 1 2   years = Compound interest for 1 year - Simple interest for next 1 2   year
⇒  Interest = 8000 – 4400
⇒  Interest = Rs.12400
Also calculating amount,
Amount = principal + interest
⇒Amount= 80000+ 12400  ⇒Amount=Rs. 92400  
Hence, amount after 1 1 2   years is Rs 92400.
Therefore, the answer is option (4).
 
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Arif took a loan of Rs. 80,000 from a bank. If the rate of interest is 10% per annum, find the difference in amounts he would be paying after 1 1 2  years if the interest is compounded annually.