Rohan borrowed a sum of Rs.1,20,000 from a financial institution at an annual compound interest rate of 8% for a tenure of 2 years. He invested $\frac{3}{4}$th of this borrowed amount into a mutual fund project that yields 10% compound interest per annum compounded annually for 2 years. If he retains the remaining portion of the money with himself, calculate his total net gain or loss after 2 years.

The correct option is Rs.1068 loss.

Step 1: Calculate the total amount Rohan has to repay to the financial institution after 2 years.

Rohan borrowed a principal amount of Rs. 1,20,000 at a compound interest rate of 8% per annum for 2 years.

The formula for the total compound interest amount is:

$A=P{(1+\frac{r}{100})}^n$

Substituting the values:

$A_{\text{repay}}=120000{(1+\frac{8}{100})}^2$

$A_{\text{repay}}=120000{\left(1.08\right)}^2$

$A_{\text{repay}}=120000\times 1.1664=\text{Rs. 1,39,968}$

Step 2: Calculate the amount invested in the mutual fund and the return after 2 years.

Rohan invested $\frac{3}{4}$th of the borrowed sum into a mutual fund project:

$\text{Invested Amount}=\frac{3}{4}\times 120000=\text{Rs. 90,000}$

The mutual fund yields 10% compound interest per annum for 2 years:

$A_{\text{invested}}=90000{(1+\frac{10}{100})}^2$

$A_{\text{invested}}=90000{\left(1.1\right)}^2$

$A_{\text{invested}}=90000\times 1.21=\text{Rs. 1,08,900}$

Step 3: Calculate the retained amount.

Rohan retained the remaining portion of the money with himself (which generates no interest):

$\text{Retained Amount}=120000-90000=\text{Rs. 30,000}$

Step 4: Calculate the total money Rohan has after 2 years.

$\text{Total Money Available}=\text{Amount from Mutual Fund}+\text{Retained Amount}$

$\text{Total Money Available}=108900+30000=\text{Rs. 1,38,900}$

Step 5: Calculate Rohan's total net gain or loss.

$\text{Net Outcome}=\text{Total Money Available}-\text{Total Amount to Repay}$

$\text{Net Outcome}=138900-139968=-\text{Rs. 1,068}$

Since the result is negative, Rohan suffers a total net loss of Rs. 1068.