Mohan borrows a sum of ₹4,22,092 at the rate of 20% per annum simple interest. At the end of the first year, he repays ₹21,679 towards return of principal amount borrowed. If Mohan 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?

The correct option is 5,64,914.

To find the total amount Mohan pays at the end of the second year to clear all his dues, we can break down the calculation step-by-step:

Step 1: Calculate the interest accrued in the first year
Mohan borrows a principal amount ($P_1$) of ₹4,22,092 at a simple interest rate of 20% per annum.
Interest accrued at the end of the first year ($I_1$) is:

$I_1=P_1\times R\times T$

$I_1=\mathrm{4,22,092}\times \frac{20}{100}\times 1=\text{₹}\mathrm{84,418.4}$

Step 2: Calculate the remaining principal for the second year
At the end of the first year, Mohan repays ₹21,679 towards the principal amount borrowed.
Therefore, the outstanding principal for the second year ($P_2$) becomes:

$P_2=\mathrm{4,22,092}-\mathrm{21,679}=\text{₹}\mathrm{4,00,413}$

Step 3: Calculate the interest accrued in the second year
The simple interest for the second year is calculated on the remaining principal ($P_2$):

$I_2=P_2\times R\times T$

$I_2=\mathrm{4,00,413}\times \frac{20}{100}\times 1=\text{₹}\mathrm{80,082.6}$

Step 4: Calculate the total payment at the end of the second year
To clear all pending dues at the end of the second year, Mohan must pay the remaining principal along with the interest accumulated over both the first and second years:
Total Payment = Remaining Principal ($P_2$) + First Year Interest ($I_1$) + Second Year Interest ($I_2$)

$\text{Total Payment}=\mathrm{4,00,413}+\mathrm{84,418.4}+\mathrm{80,082.6}$

$\text{Total Payment}=\text{₹}\mathrm{5,64,914}$