Compound Interest

• (since is in decimal form)
• (since it's compounded semiannually)

• Principal Amount ( ): ₹200,000
• Annual Interest Rate ( ): 6%
• Number of Payments ( ): 5 years, or 60 months
• Monthly Interest Rate ( ):

To determine how the piece of paper will appear when unfolded, visualize each step:

1. Understanding the Fold:
   When a piece of paper is folded, any cut made will be mirrored or duplicated symmetrically across the fold line. It's vital to consider both the cut's shape and its placement relative to the folded line.
2. Analyzing the Cut:
   Inspect the given folded paper with the cut. Identify whether the cut intersects, touches, or runs parallel to the fold line. These details determine how the cut will translate when unfolded.
3. Unfolding the Paper:
   Visualize the fold opening up. Any shape cut through the folded layer will appear mirrored on the opposite side of the original fold line. This results from the symmetrical properties of folding.
4. Identifying the Correct Option:
   Compare the visualized unfolded shape with the provided options. The correct option will display a symmetric arrangement of cuts across the original fold line.

For the current scenario, the correct appearance when unfolded is:

• Cost Price of the car = ₹8,50,000
• Scrap Value = ₹1,25,000
• Annual Depreciation = ₹1,45,000

1. Calculate the total depreciation:
2. Substitute back into the equation:
3. Solve for Useful Life:
4. Calculate:

1. Identify the nominal annual rate (APR):APR = 8%
2. Determine the number of compounding periods per year:n = 2 (since it's semi-annually)
3. Convert the nominal rate to a decimal for calculations:r =
4. Use the formula for effective annual rate:
5. Substitute the known values into the formula:
6. Simplify the expression:
7. Calculate the exponent:
8. Subtract 1:
9. Convert the effective rate back to percentage:

Thus, the effective annual rate equivalent to a nominal rate of 8% compounded semi-annually is 8.16%.

• is the value of the car after years.
• is the present value of the car, which is ₹6,25,000.
• is the rate of depreciation, which is or .
• is the number of years, which is .

To find the effective rate of interest when the nominal rate is compounded half-yearly, we will apply the formula for the effective rate of interest:

Where:

• (nominal rate of interest)
• (number of compounding periods per year, since it is compounded half-yearly)

Substitute these values into the formula:

Convert this decimal into a percentage:

Therefore, the effective rate of interest is .

• (future value)
• (quarterly interest rate)
• (total number of quarters)

The accumulated value of the sinking fund is calculated using the formula:

Here:

- ,

- ,

- ,

- .

Substitute into the formula:

The surplus is:

The formula for EMI is:

.

Here:

,

,

The given value .

The EMI for each property is calculated as:

.

For Property P:

For Property Q:

For Property R:

For Property S:

Final Matching: (A) P (I) 25,600 (B) Q (III) 32,000 (C) R (IV) 35,200 (D) S (II) 38,400

Thus, the correct option is (2).