Question : A person borrows Rs.1,00,000 from a bank at 10% per annum simple interest and clears the debt in five years. If the instalment paid at the end of the first, second, third, and fourth years to clear the debt are Rs.10,000, Rs. 20,000, Rs. 30,000, and Rs. 40,000, respectively, what amount should be paid at the end of the fifth year to clear the debt?
Option 1: Rs. 38,250
Option 2: Rs. 39,490
Option 3: Rs. 40,450
Option 4: Rs. 36,450
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Correct Answer: Rs. 39,490
Solution :
Given, A person borrows Rs.1,00,000 from a bank at 10% per annum.
1st year interest = 100000 × 10% = Rs. 10,000
The instalment paid at the end of the first year = Rs. 10,000
Principal amount for 2nd year = 100,000 – 10000 + 10000 = Rs. 1,00,000
So 2nd year interest = 1,00,000 × 10% = Rs. 10,000
The instalment paid at the end of the second year = Rs. 20,000
Principal amount for 3rd year = 1,00,000 – 20,000 + 10,000 = Rs. 90,000
So 3rd year interest = 90,000 × 10% = Rs. 9,000
The instalment paid at the end of the third year = Rs. 30,000
Principal amount for 4th year = 90,000 – 30,000 + 9000 = Rs. 69,000
So 4th year interest = 69,000 × 10% = Rs. 6,900
The instalment paid at the end of the fourth year = Rs. 40,000
Principal amount for 5th year = 69000 – 40000 + 6900 = Rs. 35900
So 5th year interest = 35,900 × 10% = Rs. 3590
In 5th year he has to pay the total amount (Principal + Interest for the fifth) as the remaining Amount
= 35900 + 3590 = 39,490
Hence, the correct answer is Rs. 39,490.
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