Pranav borrows a sum of ₹335180 at the rate of 13% per annum simple interest. At the end of the first year, he repays ₹23060 towards return of principal amount borrowed. If Pranav clears all pending dues at the end of the second year, including interest payment that accrued during the first year, how much does he pay (in ₹) at the end of the second year?

Question

Accepted Answer

Step 1: Calculate interest for the first year on the entire principal.
Interest = Principal × Rate × Time / 100
= 335180 × 13 × 1 / 100 = ₹43573.4

Step 2: At the end of the first year, Pranav repays ₹23060 towards principal.
Remaining principal after first year = 335180 - 23060 = ₹312120

Step 3: Interest for the second year is calculated on the remaining principal.
Interest for second year = 312120 × 13 × 1 / 100 = ₹40575.6

Step 4: Total amount to be paid at the end of the second year includes:
- Remaining principal: ₹312120
- Interest for first year (not yet paid): ₹43573.4
- Interest for second year: ₹40575.6

Total payment at end of second year = 312120 + 43573.4 + 40575.6 = ₹396269

Step 5: However, the question states that the interest accrued during the first year is to be paid at the end of the second year along with clearing all dues. The repayment of ₹23060 at the end of the first year was only towards principal, so interest for the first year is still pending and must be paid at the end of the second year.

Therefore, total amount to pay at end of second year = Remaining principal + Interest for first year + Interest for second year
= 312120 + 43573.4 + 40575.6 = ₹396269

Checking options, ₹396269 matches option 3, but the answer given is option 2 (₹393949). Let's re-examine calculations for any mistakes.

Recalculation:
Interest first year = 335180 × 13% = 43573.4
Principal repaid after first year = 23060
Remaining principal = 335180 - 23060 = 312120
Interest second year = 312120 × 13% = 40575.6
Total payment at end of second year = 312120 + 43573.4 + 40575.6 = 396269

Since the answer given is 393949, let's check if the interest for the second year is calculated on the original principal instead of remaining principal:
Interest second year (on original principal) = 335180 × 13% = 43573.4
Total payment = 312120 + 43573.4 + 43573.4 = 399266.8 (not matching any option)

Alternatively, if the interest for the second year is calculated on the principal after repayment (312120) but the repayment of ₹23060 is considered at the end of the second year, not the first year, then:
Interest first year = 335180 × 13% = 43573.4
Interest second year = 335180 × 13% = 43573.4
Total interest = 87146.8
Total principal = 335180
Total amount = 335180 + 87146.8 = 422326.8 (not matching)

Since the question states repayment of ₹23060 at the end of first year towards principal, the remaining principal for second year interest calculation is correct.

Therefore, the correct total payment at the end of second year is ₹396269 (option 3).

Hence, the correct answer is option 3: ₹396269.

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