A borrowed ₹28,500 at 8% p.a. interest, compounded annually. If ₹5,780 was paid at the end of the first year, what is the outstanding amount at the end of the second year?
A. 27000
B. 33242.4
C. 30780
D. 27462.4
Answer (2)
To solve this problem, we need to determine the outstanding amount at the end of the second year after considering the interest and the payment made.
Initial Details :
Principal Amount, P = ₹28,500
Annual Interest Rate, r = 8% or 0.08 as a decimal
First Year Payment = ₹5,780
Compute the Amount after the First Year : The formula for compound interest is given by: A = P ( 1 + r ) n Where:
A is the amount after n years,
n is the number of years, here n = 1 .
Substitute the given values: A 1 = 28 , 500 × ( 1 + 0.08 ) 1 = 28 , 500 × 1.08 = 30 , 780
After the first year, the amount becomes ₹30,780.
Subtract the Payment Made : After making the payment of ₹5,780, we subtract it from the first year's amount: Outstanding After First Year = 30 , 780 − 5 , 780 = 25 , 000
Compute the Amount at the End of the Second Year : Again, apply the compound interest formula for the second year using the new principal of ₹25,000: A 2 = 25 , 000 × ( 1 + 0.08 ) 1 = 25 , 000 × 1.08 = 27 , 000
At the end of the second year, the outstanding amount is ₹27,000.
Therefore, the outstanding amount at the end of the second year is ₹27,000. The correct answer is A. 27000 .
The outstanding amount at the end of the second year after considering the compound interest and payment made is ₹27,000. Therefore, the correct option is A. 27000.
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