DSSSB TGT CS 2023 Shift 2 – Question 052

A loan of ₹ 10,200 is to be paid back in two equal half-yearly instalments. If the rate of interest is 8% p.a., compounded half-yearly, then what is the total interest charged in this scheme?

• ₹ 600
• ₹ 616
• ₹ 620
• ₹ 636

Step 1: Determine the rate per compounding period:
Annual rate = 8% p.a., compounded half-yearly.
Half-yearly rate \(r = \frac{8\%}{2} = 4\% = \frac{4}{100} = \frac{1}{25}\).

Step 2: Set up the instalment formula:
Let each equal half-yearly instalment be \(x\).
The sum of the present values of the two instalments equals the borrowed loan amount (₹ 10,200):
\[ \frac{x}{1 + r} + \frac{x}{(1 + r)^2} = 10,200 \]
Since \(1 + r = 1 + \frac{1}{25} = \frac{26}{25}\):
\[ x \left[ \frac{25}{26} + \left(\frac{25}{26}\right)^2 \right] = 10,200 \]
\[ x \cdot \frac{25}{26} \left[ 1 + \frac{25}{26} \right] = 10,200 \]
\[ x \cdot \frac{25}{26} \cdot \frac{51}{26} = 10,200 \]

Step 3: Solve for each instalment \(x\):
Notice that \(10,200 = 51 \times 200\):
\[ x \cdot \frac{25}{676} = 200 \]
\[ x = \frac{200 \times 676}{25} = 8 \times 676 = ₹ 5,408 \]

Step 4: Calculate the total interest charged:
\[ \text{Total Amount Paid} = 2 \times 5,408 = ₹ 10,816 \]
\[ \text{Total Interest} = \text{Total Amount Paid} – \text{Loan Principal} = 10,816 – 10,200 = ₹ 616 \]
Hence, the correct answer is option b).