1. The formula for simple interest (SI) is P * R * T / 100, where P is the Principal, R is the annual interest Rate, and T is the Time in years. 2. We are given SI = $450, R = 2.5%, and T = 3 years. We need to find P. 3. Rearranging the formula to solve for P: P = (SI * 100) / (R * T). 4. Substitute the given values into the rearranged formula: P = (450 * 100) / (2.5 * 3). 5. Calculate the denominator: 2.5 * 3 = 7.5. 6. Calculate the numerator: 450 * 100 = 45000. 7. Perform the division: P = 45000 / 7.5 = 6000. 8. Therefore, the principal amount Mr. Khan invested was $6000. Why others are wrong: A — This is the correct principal amount. B — This results from calculating SI * R * T (450 * 2.5 * 3), failing to divide by 100 for the percentage rate. C — This results from calculating P = SI / (R/100) (450 / 0.025), thereby ignoring the time factor (3 years). D — This results from an arithmetic error during the final division, specifically treating 7.5 as 10 (45000 / 10 = 4500) or another miscalculation.

1. Identify the given values: Total Amount (A) = $7,000, Annual Rate (R) = 8% (or 0.08), Time (T) = 5 years. 2. The formula for the total amount repaid with simple interest is A = P + I, where I = (P * R * T) / 100. 3. Substitute the simple interest formula into the total amount formula: A = P + (P * R * T) / 100, which can be rearranged to A = P * (1 + (R * T) / 100). 4. Plug in the known values: $7,000 = P * (1 + (8 * 5) / 100). 5. Simplify the expression: $7,000 = P * (1 + 40 / 100) = P * (1 + 0.40) = P * 1.40. 6. Solve for P: P = $7,000 / 1.40. 7. P = $5,000. Why others are wrong: A — This option results from an incorrect calculation of the principal relative to the total repayment. C — This option results from an incorrect calculation of the principal, overestimating it compared to the correct amount. D — This option results from a significant miscalculation of the principal amount or the interest component.

The formula for Simple Interest (SI) is P * R * T, where P is Principal, R is Rate, and T is Time. We are given: SI = $1,890 R = 4.5% = 0.045 (as a decimal) T = 7 years We need to find P. Rearrange the formula: P = SI / (R * T) P = $1,890 / (0.045 * 7) P = $1,890 / 0.315 P = $6,000 Why others are wrong: A — This result would occur if the interest were divided by 0.45 (e.g., $1,890 / 0.45 = $4,200), possibly from a calculation error where (0.045 * 7) was approximated or miscalculated as 0.45. B — This option is likely a distractor from a minor calculation error or misinterpretation of the rate (e.g., if the rate was approximated as 5%, P = $1,890 / (0.05 * 7) = $5,400). D — This amount ($6,000 + $1,890) represents the total "Amount" (Principal + Interest) after 7 years, not the initial principal.

1. Calculate Liam's simple interest: Principal ($5,000) × Rate (0.04) × Time (3 years) = $600. 2. Calculate Olivia's simple interest: Principal ($4,500) × Rate (0.05) × Time (3 years) = $675. 3. Compare the amounts: Olivia earned $675 and Liam earned $600. 4. The difference is $675 - $600 = $75. Olivia earned $75 more interest than Liam. Why others are wrong: B — Incorrectly states Liam earned more interest. C — Fails to account for the differences in principal and rates, leading to different interest earnings. D — Contains an arithmetic error in calculating the difference between the two interest amounts.

1. Identify the given values: Simple Interest (SI) = $540, Time (T) = 3 years, Rate (R) = 6% per annum. 2. Recall the formula for Simple Interest: SI = (P * R * T) / 100. 3. Rearrange the formula to solve for Principal (P): P = (SI * 100) / (R * T). 4. Substitute the given values into the formula: P = (540 * 100) / (6 * 3). 5. Calculate the product in the denominator: 6 * 3 = 18. 6. Calculate the numerator: 540 * 100 = 54000. 7. Perform the division: P = 54000 / 18 = 3000. 8. Therefore, the original principal amount was $3000. Why others are wrong: A — Incorrect. A principal of $2700 would yield $486 in simple interest over 3 years at 6% (2700 * 6 * 3 / 100 = 486). B — This is the correct principal amount. C — Incorrect. A principal of $3240 would yield $583.20 in simple interest over 3 years at 6% (3240 * 6 * 3 / 100 = 583.20). D — Incorrect. A principal of $3600 would yield $648 in simple interest over 3 years at 6% (3600 * 6 * 3 / 100 = 648).