The Assertion is true because businesses commonly require loans to finance: machinery, inventory, working capital, expansion. The Reason is false because many individuals do not have sufficient savings to purchase expensive assets such as houses or cars outright. They usually depend on loans or mortgages. Hence, the Assertion is true but the Reason is false. Therefore, Option B is correct.

A loan is money borrowed from a lender for a specified period. The borrower agrees to: repay the principal, pay interest, complete repayment within the agreed loan term. Therefore, the Assertion is true, and the Reason correctly explains why repayment occurs within a defined period. Hence, Option C is correct.

The principal is the original amount borrowed from the lender. The final repayment generally consists of: repayment of the principal, and payment of interest. Therefore, the principal is not the final amount repaid. Thus, the Assertion is false, and the Reason is true. Hence, Option D is correct.

The initial amount borrowed is called the principal, not the interest. Interest is the additional amount paid to the lender for using the borrowed money. Mathematically, Interest = Total Amount Repaid − Principal Hence, Statement I is incorrect. Statement II correctly describes interest. Therefore, Option A is correct.

The rate of interest is the percentage charged on the principal amount for a specified period, usually one year. It depends directly on: the principal, the interest rate, the loan duration. Therefore, it is not a fixed fee independent of the loan amount. Hence, Option B is correct.

In an amortized loan: (P) denotes the principal amount borrowed. (n) denotes the total number of monthly instalments. (R) denotes the monthly EMI. Total interest equals the total repayment minus the principal. Although the numerical values in List II are omitted in the question, the intended matching provided is: 1 → c 2 → a 3 → d 4 → b Therefore, Option A is the correct answer.

The abbreviation EMI stands for Equated Monthly Instalment. Thus, the correct order is: 1. Equated 2. Monthly 3. Instalment Hence, 1 → 3 → 2 Therefore, Option D is correct.

Total number of monthly payments: 5 × 12 = 60 Total amount paid: Total Paid = 5000 × 60 = ₹3,00,000 Therefore, Total Amount Paid = ₹3,00,000 Hence, Option A is correct.

In an amortized loan, interest for each period is calculated on the outstanding principal, not on the original loan amount. As EMIs are paid, the outstanding balance decreases, the interest portion decreases, the principal repayment portion increases. Therefore, interest is always computed on the remaining loan balance. Hence, Option B is correct.

In the reducing-balance method, interest is calculated on the outstanding loan balance. At the beginning of the loan: the outstanding balance is highest, therefore the interest charged is also highest. Since the EMI is fixed, a larger portion goes toward interest, and a smaller portion reduces the principal. As the loan progresses, the outstanding balance decreases, causing the interest portion to decrease and the principal repayment to increase. Hence, Option C is correct.

Using the flat-rate formula, I = P × r × n Given, P = ₹5,00,000, r = 8% = 0.08, n = 6 years Substituting, I = 5,00,000 × 0.08 × 6 = 2,40,000 Therefore, I = ₹2,40,000 Hence, Option D is correct.

Under the Flat Rate Method, interest is calculated on the original principal throughout the loan period, regardless of the outstanding balance. The interest formula is I = P × r × n where (P) remains the original loan amount. In contrast, the Reducing Balance Method calculates interest only on the unpaid balance after each EMI. Therefore, Option A is correct.

Given, P = ₹5,00,000, I = ₹2,40,000, n = 72 months Total repayment: P + I = 5,00,000 + 2,40,000 = 7,40,000 EMI is: EMI = 7,40,000 / 72 = 10,277.77 Therefore, EMI ≈ ₹10,277.77 or approximately ₹10,278. Hence, Option B is correct.

Under the Flat Rate Method, interest is calculated on the original loan amount throughout the loan period. The EMI formula is EMI = (P + I) / n where (P) = Principal, (I) = Total interest, (n) = Number of monthly instalments. The reducing-principal method applies only to the reducing-balance (amortization) method. Hence, Option C is correct.

According to the passage, the principal outstanding at the beginning of any period is equal to the present value of all remaining instalments. Mathematically, Outstanding Principal = R ā₍ₙ₋ₖ₊₁₎|ᵢ where (R) = EMI, (a_{\overline{(n-k+1)}|i}) = Present value annuity factor. Thus, the outstanding principal represents the current value of the remaining payments. Hence, Option D is correct.

In financial mathematics: Ordinary annuity → Payments occur at the end of each period. Annuity due → Payments occur at the beginning of each period. Since the passage states that loan payments are made at the end of each period, the loan follows the ordinary annuity model. This model is commonly used in loan amortization calculations. Hence, Option A is correct.

The outstanding principal at the beginning of the (k^{\text{th}}) period is calculated as the present value of the remaining EMIs, given by R × ā₍ₙ₋ₖ₊₁₎|ᵢ Thus, the Assertion is correct. The Reason is false because the outstanding principal is not the sum of past payments. Instead, it represents the remaining unpaid balance of the loan, calculated from the future instalments yet to be paid. Therefore, Option B is correct.

For an amortized loan, Total Interest = nR − P where (P) = Loan amount, (n) = Number of instalments, (R) = EMI. Although the numerical entries in List II are omitted, the intended correspondence provided in the question is: 1 → d 2 → a 3 → c 4 → b Hence, Option A is correct.

Given: EMI ₹12,668) Loan period (=10) years Number of monthly instalments: n = 10 × 12 = 120 Therefore, Total Paid = 12,668 × 120 = ₹15,20,160 Thus, Total Amount Paid = ₹15,20,160 Hence, Option D is correct.

The total repayment is nR = 120 × 12,668 = ₹15,20,160 Total interest is Interest = nR − P Substituting, Interest = 15,20,160 − 10,00,000 = ₹5,20,160 Therefore, Total Interest = ₹5,20,160 Hence, Option A is correct.