Question 1

Find rate from true discount: The true discount on a sum of ₹ 50,000 for 4 years is ₹ 2,000 at a certain simple-interest rate per annum. Find the annual rate of interest.

Accepted Answer

Introduction / Context: True discount TD for a future sum S due after t years at rate r (per annum) under simple interest is TD = S * r * t / (1 + r * t). Knowing TD, S, and t allows solving for r. This is a standard algebraic inversion. Given Data / Assumptions: S (future sum) = ₹ 50,000. t = 4 years. TD = ₹ 2,000. Concept / Approach: Let u = r * t. Then TD = S * u / (1 + u). Solve u from 2,000 = 50,000 * u / (1 + u), then compute r = u / t. Step-by-Step Solution: 2,000(1 + u) = 50,000u ⇒ 2,000 = 48,000u ⇒ u = 2,000 / 48,000 = 1/24 ≈ 0.0416667.r = u / t = (1/24) / 4 = 1/96 ≈ 0.0104167 ≈ 1.04%.Closest standard rate in the options = 1%. Verification / Alternative check: Using r ≈ 1.0417% gives TD ≈ 50,000 * (0.010417*4) / (1 + 0.010417*4) ≈ 2,000; rounding to the nearest listed rate is appropriate. Why Other Options Are Wrong: 1.5%, 2%, and 5% produce TD far from ₹ 2,000 for 4 years; 0.75% underestimates. Common Pitfalls: Omitting the denominator (1 + r t) and equating TD to S r t, which would overstate the rate. Final Answer: 1%

Question 2

Present worth at simple interest: Find the present worth of Rs. 264 due in 2 years when simple interest is reckoned at 5% per annum.

Accepted Answer

Introduction / Context: Present worth (PW) is the current value of a future sum under simple interest. The relation is PW = S / (1 + r * t), where S is the future amount, r is annual simple interest rate, and t is time in years. Given Data / Assumptions: S = Rs. 264 (due after 2 years). r = 5% per annum. t = 2 years. Concept / Approach: Apply PW formula directly: divide the future amount by (1 + r t). Ensure r is expressed as a decimal and time is in years. Step-by-Step Solution: 1 + r t = 1 + 0.05 * 2 = 1.10.PW = 264 / 1.10 = Rs. 240. Verification / Alternative check: Re-accumulating PW at 5% for 2 years: 240 * (1 + 0.10) = 240 * 1.10 = 264; consistent. Why Other Options Are Wrong: Rs. 260 and Rs. 252 are too high; Rs. 360 and Rs. 540 are unrelated to discounting. Common Pitfalls: Multiplying instead of dividing by (1 + r t); using compound interest when simple interest is specified. Final Answer: Rs. 240

Question 3

Present worth with fractional time: What is the present worth of Rs. 272.61 due in 2 years 73 days at 7 1/2% per annum simple interest? (Assume 365 days in a year.)

Accepted Answer

Introduction / Context: Present worth calculation with simple interest and a non-integer time requires converting the extra days into a fraction of a year. Then apply PW = S / (1 + r t). Careful handling of the day fraction ensures accuracy. Given Data / Assumptions: S = Rs. 272.61 due after 2 years and 73 days. r = 7.5% per annum = 0.075. Year length assumed = 365 days. Concept / Approach: Convert 73 days to 73/365 years. Total t = 2 + 73/365 = 2.2 years. Then PW = 272.61 / (1 + 0.075 * 2.2). Step-by-Step Solution: t = 2 + 73/365 = 2.2 years.1 + r t = 1 + 0.075 * 2.2 = 1 + 0.165 = 1.165.PW = 272.61 / 1.165 = Rs. 234.00 (exact). Verification / Alternative check: Re-accumulate: 234 * 1.165 = 272.61, confirming exactness to the paise. Why Other Options Are Wrong: Rs. 254 and Rs. 240 are too high; Rs. 334 is far off; “None of these” is unnecessary because an exact match exists. Common Pitfalls: Using 360 days instead of 365 without instruction, or omitting the 73-day fraction entirely. Final Answer: Rs. 234

Question 4

TD is less than SI by a known amount: The true discount on a certain sum due after 2 1/2 years at 6% per annum is less than the simple interest on the same sum and period by Rs. 81. Find the sum due (face value).

Accepted Answer

Introduction / Context: For a future sum S at rate r and time t (simple interest), the difference SI − TD equals S * (r t)^2 / (1 + r t). When this difference is given, we can solve for S directly. Here, “TD is less than SI by Rs. 81” means SI − TD = 81. Given Data / Assumptions: r = 6% per annum = 0.06. t = 2.5 years ⇒ r t = 0.06 * 2.5 = 0.15. SI − TD = Rs. 81. Concept / Approach: Use SI − TD = S * (r t)^2 / (1 + r t). Rearrange to S = (SI − TD) * (1 + r t) / (r t)^2 and substitute the numbers. Step-by-Step Solution: Compute factor = (r t)^2 / (1 + r t) = (0.15)^2 / 1.15 = 0.0225 / 1.15 ≈ 0.0195652.S = 81 / 0.0195652 ≈ Rs. 4,140. Verification / Alternative check: Back-check: 4,140 * 0.0195652 ≈ 81, so the relation holds. Why Other Options Are Wrong: 4,240, 4,150, and 4,250 are off the exact computation; 4,000 is also incorrect. Common Pitfalls: Misinterpreting “less than” and using TD − SI, or forgetting the denominator (1 + r t) in the difference formula. Final Answer: Rs. 4140

Question 5

Find rate percent from true discount: The true discount on Rs. 340 due 5 years hence is Rs. 40. What is the simple-interest rate per annum?

Accepted Answer

Introduction / Context: True discount (TD) relates the future sum S, rate r, and time t under simple interest via TD = S * r * t / (1 + r * t). With S, TD, and t known, solve for r. This applies to bills due at a future date where TD is the deduction to obtain present worth. Given Data / Assumptions: S = Rs. 340 (amount due after 5 years). TD = Rs. 40. t = 5 years. Concept / Approach: Let u = r * t. Then TD = S * u / (1 + u). Solve u from 40 = 340 * u / (1 + u), then obtain r = u / t. Convert the decimal to a mixed fraction percentage for clarity. Step-by-Step Solution: 40(1 + u) = 340u ⇒ 40 = 300u ⇒ u = 40/300 = 2/15 ≈ 0.133333.r = u / t = (2/15) / 5 = 2/75 ≈ 0.0266667 = 2.666…%.Therefore rate ≈ 2 2/3% per annum. Verification / Alternative check: Substitute r = 2 2/3% back: u = r t = 2/75 * 5 = 2/15; TD = 340 * (2/15) / (1 + 2/15) = 340 * (2/15) / (17/15) = 340 * (2/17) = 40. Why Other Options Are Wrong: 3%, 3 1/3%, and 3 2/3% are higher than required; 2% is lower. Only 2 2/3% satisfies the equation exactly. Common Pitfalls: Dropping the (1 + r t) term; treating TD as S r t, which would give an inflated rate. Final Answer: 2 2/3%

Question 6

In simple interest and true discount problems: The true discount (TD) on a bill of $161 due after 2 years and 6 months (i.e., 2.5 years) is $21. Calculate the annual rate of interest (per annum) at which this true discount is computed.

Accepted Answer

Introduction / Context: This problem tests the connection between True Discount (TD), present worth, and the simple interest rate for a given time. We use the standard TD relation with simple interest to find the annual rate. Given Data / Assumptions: Face value F = 161 True discount TD = 21 Time t = 2.5 years Simple interest framework; TD is computed at the same rate r per annum. Concept / Approach: For simple interest, TD = F * (r * t) / (1 + r * t). Let x = r * t. Then TD/F = x/(1 + x). Solve for x, then r = x/t. Step-by-Step Solution: Let x = r * t. TD/F = x/(1 + x) = 21/161. Cross-multiply: 21(1 + x) = 161x. 21 + 21x = 161x → 21 = 140x → x = 21/140 = 0.15. Since x = r * t and t = 2.5, r = x / t = 0.15 / 2.5 = 0.06 = 6%. Verification / Alternative check: Compute present worth P = F/(1 + r*t) = 161/(1 + 0.06*2.5) = 161/1.15 = 140. TD = F - P = 161 - 140 = 21, which matches the given TD. Why Other Options Are Wrong: 4% and 5% give smaller x and thus smaller TD than 21; 8% and 10% give larger x, producing TD greater than 21. Only 6% satisfies the relation exactly. Common Pitfalls: Confusing TD with simple interest on face value; forgetting the denominator (1 + r*t); or mixing years and months without converting to years. Final Answer: 6%

Question 7

A certain sum is due after 2 years. Its true discount is ₹ 1800, and the simple interest on the same sum (for the same time and rate) is ₹ 2232. Find the sum due (the face value).

Accepted Answer

Introduction / Context: This question connects True Discount (TD) and Simple Interest (SI) on the same face value over the same time. Using TD and SI together lets us solve for the face value efficiently. Given Data / Assumptions: TD = 1800 SI on the same face value and time = 2232 Time and rate are the same for both measures (simple interest basis). Concept / Approach: Let face value be F and x = r*t. Then: TD = F * x / (1 + x) SI on F = F * x Using both equations eliminates x and gives F directly. Step-by-Step Solution: From SI: F * x = 2232 → x = 2232 / F. TD = F * x / (1 + x) = 1800. So, 2232 / (1 + 2232/F) = 1800. 2232 = 1800 + (1800 * 2232)/F. 432 = (1800 * 2232)/F → F = (1800 * 2232)/432 = 9300. Verification / Alternative check: Compute x = SI/F = 2232/9300 = 0.24. Then TD = F * x/(1 + x) = 9300 * 0.24/1.24 = 2232/1.24 = 1800, confirming correctness. Why Other Options Are Wrong: Values like 9450 or 9600 give inconsistent x, resulting in TD not equal to 1800. 9350 and 9000 likewise fail the joint TD–SI condition. Common Pitfalls: Treating TD as SI on face value (it is not); ignoring the (1 + x) denominator; or attempting to use present worth directly without eliminating variables. Final Answer: ₹ 9300

Question 8

The difference between the simple interest and the true discount on a certain sum for 2 years at 15% per annum (simple interest) is ₹ 45. Determine the sum due (face value).

Accepted Answer

Introduction / Context: This problem compares simple interest on the face value with the corresponding true discount at the same rate and time. Their difference allows us to compute the face value directly. Given Data / Assumptions: Time t = 2 years Rate r = 15% per annum Difference (SI − TD) = ₹ 45 Concept / Approach: With x = r*t, SI on the face value F is F * x and TD is F * x / (1 + x). Hence: SI − TD = F * x − F * x/(1 + x) = F * x^2/(1 + x). We solve for F. Step-by-Step Solution: x = r*t = 0.15 * 2 = 0.30. SI − TD = F * x^2/(1 + x) = F * 0.09/1.30. Given 45 = F * (0.09/1.30) → F = 45 * 1.30 / 0.09. F = 58.5 / 0.09 = 650. Verification / Alternative check: Compute SI = F * x = 650 * 0.30 = 195. TD = F * x/(1 + x) = 650 * 0.30/1.30 = 150. SI − TD = 195 − 150 = 45, exactly as given. Why Other Options Are Wrong: 675, 700, 625, 600 do not reproduce the exact 45 difference when plugged into SI and TD formulas at 15% for 2 years. Common Pitfalls: Forgetting to square x in the numerator; using present worth instead of face value; or mixing up SI − TD with TD − SI. Final Answer: ₹ 650

Question 9

Simple interest on ₹ 2000 at 5% per annum equals the true discount on ₹ 2500 for the same time and at the same rate. Find the time (in years).

Accepted Answer

Introduction / Context: Here the equality of a simple interest on one principal and the true discount on another principal (same time and rate) allows solving for time without finding the rate separately. Given Data / Assumptions: SI on ₹ 2000 at 5% per annum for time t equals TD on ₹ 2500 at the same rate and time. Concept / Approach: SI = P * r * t. TD = F * (r * t)/(1 + r * t). Set these equal and solve for t (note r cancels). Step-by-Step Solution: 2000 * 0.05 * t = 2500 * (0.05 * t) / (1 + 0.05 * t). 100 t = 125 t/(1 + 0.05 t). Cross-multiply: 100 t (1 + 0.05 t) = 125 t. 100 + 5 t = 125 → 5 t = 25 → t = 5 years. Verification / Alternative check: Let t = 5. SI on 2000 = 2000 * 0.05 * 5 = 500. TD on 2500 with r t = 0.25 is 2500 * 0.25/1.25 = 500. Match confirmed. Why Other Options Are Wrong: Any time other than 5 years fails the equality because the TD has the denominator (1 + r t), which uniquely balances at t = 5 under these principals. Common Pitfalls: Cancelling t too early (t ≠ 0); ignoring the (1 + r t) factor; or equating SI on face value directly to SI on present worth instead of TD. Final Answer: 5 years

Question 10

On ₹ 371, the true discount for a certain time is ₹ 21. For double that time at the same rate, what will be the true discount on the same amount?

Accepted Answer

Introduction / Context: True Discount (TD) varies nonlinearly with time because TD = F * x/(1 + x) where x = r * t. Doubling time doubles x but not TD linearly; hence we evaluate TD at 2x. Given Data / Assumptions: F = 371 TD at time t = 21 Need TD at 2t, same rate r Concept / Approach: From TD = F * x/(1 + x), obtain x at time t, then compute TD at 2x. Step-by-Step Solution: 21 = 371 * x/(1 + x) → 21(1 + x) = 371x. 21 = (371 − 21)x → x = 21/350 = 0.06. At double time, x' = 2x = 0.12. TD(2t) = 371 * 0.12/(1 + 0.12) = 371 * 0.12/1.12 = 39.75. Verification / Alternative check: Compute present worths: P(t) = 371/(1 + 0.06) = 350; P(2t) = 371/(1 + 0.12) = 331.25; TD(2t) = 371 − 331.25 = 39.75. Why Other Options Are Wrong: 39.00 and 38.85 underestimate the nonlinear increase; 40.00 overshoots; 35.75 is far from the exact computed value. Common Pitfalls: Assuming TD doubles when time doubles; forgetting the denominator (1 + x) that moderates growth. Final Answer: ₹ 39.75

Question 11

The true discount on a bill due in 9 months at 4% per annum (simple interest) is ₹ 150. Find the amount of the bill (face value).

Accepted Answer

Introduction / Context: We use the true discount formula to back-calculate the face value from TD, rate, and time. This is a direct application of TD with simple interest. Given Data / Assumptions: TD = 150 r = 4% per annum t = 9 months = 0.75 years Concept / Approach: TD = F * (r * t) / (1 + r * t). Solve for F = TD * (1 + r * t) / (r * t). Step-by-Step Solution: r * t = 0.04 * 0.75 = 0.03. F = 150 * (1 + 0.03) / 0.03 = 150 * 1.03 / 0.03 = 5150. Verification / Alternative check: Present worth P = F/(1 + r t) = 5150/1.03 = 5000. TD = F − P = 150, which matches the given data. Why Other Options Are Wrong: Values other than 5150 do not yield TD = 150 when substituted into TD = F * 0.03/1.03. Common Pitfalls: Forgetting to convert months into years or miscomputing r*t; treating TD as SI on face value instead of using the correct denominator. Final Answer: ₹ 5150

Question 12

The present worth of a bill is ₹ 1500. If the true discount on the bill is ₹ 75, find the banker’s discount (simple interest on face value for the term).

Accepted Answer

Introduction / Context: This question contrasts true discount (TD) and banker’s discount (BD). Given present worth (P) and TD, we can compute BD using a standard identity. Given Data / Assumptions: P = 1500 TD = 75 Face value F = P + TD = 1575 Concept / Approach: Banker’s discount is SI on face value: BD = F * r * t. True discount is SI on present worth: TD = P * r * t. Using r*t = TD/P, we obtain: BD = TD + (TD^2)/P. Step-by-Step Solution: Compute banker’s gain BG = BD − TD = (TD^2)/P = 75^2 / 1500 = 5625 / 1500 = 3.75. Hence BD = TD + BG = 75 + 3.75 = 78.75. Verification / Alternative check: If r*t = TD/P = 75/1500 = 0.05, then BD = F * 0.05 = 1575 * 0.05 = 78.75, matching the result. Why Other Options Are Wrong: 77.75 and 76.75 do not match the identity; 82.75 and 80.00 misapply the formula. Common Pitfalls: Confusing BD with TD; forgetting BD − TD = (TD^2)/P; or using face value instead of present worth in the TD expression. Final Answer: ₹ 78.75

Question 13

The true discount on ₹ 936 at 8% per annum (simple interest) is ₹ 36. Find the time after which the amount is due.

Accepted Answer

Introduction / Context: We determine the time of a bill given its true discount, face value, and annual rate. This uses the TD formula and solves for t. Given Data / Assumptions: F = 936 TD = 36 r = 8% per annum Concept / Approach: TD = F * (r * t)/(1 + r * t). Solve for t via x = r * t. Step-by-Step Solution: 36 = 936 * x/(1 + x). 36(1 + x) = 936x → 36 = 900x → x = 0.04. Since x = r * t = 0.08 * t, 0.08 * t = 0.04 → t = 0.5 years = 6 months. Verification / Alternative check: Present worth P = F/(1 + x) = 936/1.04 = 900. TD = F − P = 36, consistent. Why Other Options Are Wrong: 3 or 9 months do not satisfy the equation; 1 year doubles x; 8 months similarly gives a mismatch. Common Pitfalls: Forgetting to convert years to months; mixing BD with TD; dropping the (1 + x) denominator. Final Answer: 6 months

Question 14

The true discount on a bill of $2550 due after 3 months is $50. Find the banker’s discount (simple interest on the face value for 3 months).

Accepted Answer

Introduction / Context: Given true discount (TD), face value (F), and time, we can find the rate and then compute banker’s discount (BD). Given Data / Assumptions: F = 2550 TD = 50 t = 3 months = 0.25 years Concept / Approach: Use x = r * t. From TD/F = x/(1 + x), get x = TD/(F − TD). Then r = x/t, and finally BD = F * r * t. Step-by-Step Solution: x = TD/(F − TD) = 50/(2550 − 50) = 50/2500 = 0.02. r = x/t = 0.02/0.25 = 0.08 = 8% p.a. BD = F * r * t = 2550 * 0.08 * 0.25 = 51. Verification / Alternative check: Present worth P = F/(1 + x) = 2550/1.02 = 2500; TD = 50; BD must exceed TD slightly for the same term, so 51 is reasonable. Why Other Options Are Wrong: 53, 55, 57 exceed the computed SI; 50 equals TD and is not the banker’s discount. Common Pitfalls: Using BD = TD; or forgetting to convert months to years when computing r. Final Answer: $ 51

Question 15

The true discount on a bill of $5450 due in 9 months is $450. Find the annual rate of interest (per annum, simple interest).

Accepted Answer

Introduction / Context: We determine the rate from a known true discount over a given period. The time is in months and must be converted to years. Given Data / Assumptions: F = 5450 TD = 450 t = 9 months = 0.75 years Concept / Approach: With x = r * t, TD/F = x/(1 + x) → x = TD/(F − TD). Then r = x/t. Step-by-Step Solution: x = TD/(F − TD) = 450/(5450 − 450) = 450/5000 = 0.09. t = 0.75 → r = x/t = 0.09/0.75 = 0.12 = 12% p.a. Verification / Alternative check: Present worth P = 5450/(1 + 0.09) = 5000; TD = 450, consistent; and r * t = 0.12 * 0.75 = 0.09. Why Other Options Are Wrong: 12.5%, 11.5%, 13.1%, 10% do not satisfy the exact relation between TD and F for the given time. Common Pitfalls: Forgetting to convert months into years; mixing up TD with SI on face value; or solving for r without first finding x. Final Answer: 12%

Question 16

If ₹ 10 is the true discount on a bill of ₹ 110 due at the end of a certain time, then what discount would be allowed on the same amount due at the end of double the time (same rate, simple interest)?

Accepted Answer

Introduction / Context: True discount increases nonlinearly with time. Given TD at time t, we find TD at 2t using the TD formula. Given Data / Assumptions: F = 110 TD(t) = 10 Need TD(2t) at same rate Concept / Approach: TD = F * x/(1 + x) where x = r * t. First get x from TD(t), then compute TD at 2x. Step-by-Step Solution: 10 = 110 * x/(1 + x) → x = 10/(110 − 10) = 10/100 = 0.1. At double time, x' = 0.2. TD(2t) = 110 * 0.2/(1.2) = 110 * (1/6) = 18.333... ≈ ₹ 18.33. Verification / Alternative check: Present worths: P(t) = 110/1.1 = 100; P(2t) = 110/1.2 ≈ 91.666...; TD(2t) = 110 − 91.666... = 18.333..., matching. Why Other Options Are Wrong: ₹ 20 and ₹ 22 assume linear doubling; ₹ 21.81 is not the exact rational outcome; ₹ 19.80 does not follow from the formula. Common Pitfalls: Assuming TD doubles with time; ignoring the (1 + x) denominator. Final Answer: ₹ 18.33

Question 17

Find the true discount on ₹ 39.69 due in 2 years when compound interest is reckoned at 5% per annum.

Accepted Answer

Introduction / Context: Here, present worth is computed using compound interest, not simple interest. The true discount is the face value minus present worth. Given Data / Assumptions: F = 39.69 Rate = 5% compounded annually Time = 2 years Concept / Approach: Present worth with compound interest: P = F / (1 + r)^n. Then TD = F − P. Step-by-Step Solution: (1 + r)^n = (1.05)^2 = 1.1025. P = 39.69 / 1.1025 = 36.00. TD = 39.69 − 36.00 = 3.69. Verification / Alternative check: Forward check: 36 * 1.1025 = 39.69, confirming the present worth and hence TD. Why Other Options Are Wrong: 5.00, 5.69, 4.69, 3.00 do not match the exact compound discounting computation. Common Pitfalls: Using simple interest discounting for a compound interest question; rounding early; or miscomputing (1.05)^2. Final Answer: Rs. 3.69

Question 18

Find (i) the present worth and (ii) the true discount of a bill of Rs. 2420 due after 2 years at 10% compound interest per annum.

Accepted Answer

Introduction / Context: With compound interest, present worth is found by discounting the face value by (1 + r)^n. True discount equals the difference between face value and present worth. Given Data / Assumptions: F = 2420 r = 10% compounded n = 2 years Concept / Approach: P = F / (1 + r)^n. TD = F − P. Step-by-Step Solution: (1 + r)^n = 1.1^2 = 1.21. P = 2420 / 1.21 = 2000. TD = 2420 − 2000 = 420. Verification / Alternative check: 2000 grows to 2000 * 1.21 = 2420 in 2 years at 10%, so the calculation is exact. Why Other Options Are Wrong: All other pairs do not correspond to discounting at 10% compounded for 2 years. Common Pitfalls: Using simple interest discounting; or incorrectly computing 1.1^2; or swapping present worth and discount values. Final Answer: Rs. 2000, Rs. 420

Question 19

The discount on Rs. 3050 equals the simple interest on Rs. 3000 for the same time at 5% per annum. Find the time.

Accepted Answer

Introduction / Context: Here “discount” refers to true discount unless otherwise stated, and it is equated to the simple interest on another sum for the same time and rate. We solve for time. Given Data / Assumptions: TD on 3050 equals SI on 3000 Rate r = 5% per annum Time t = ? (years) Concept / Approach: TD = F * (r * t)/(1 + r * t). SI(3000) = 3000 * r * t. Set them equal and solve for t. Step-by-Step Solution: 3050 * 0.05 t /(1 + 0.05 t) = 3000 * 0.05 t. Cancel 0.05 t (t ≠ 0): 3050/(1 + 0.05 t) = 3000. 1 + 0.05 t = 3050/3000 = 1.016666... 0.05 t = 0.016666... → t = 0.3333... years = 4 months. Verification / Alternative check: Let t = 1/3 year. SI on 3000 = 3000 * 0.05 * (1/3) = 50. TD = 3050 * 0.05 * (1/3) / (1 + 0.05/3) = 50 exactly. Why Other Options Are Wrong: 6 or 3 months do not make the equality hold; “None” is incorrect since 4 months satisfies the condition. Common Pitfalls: Treating “discount” as banker’s discount; forgetting to cancel t carefully; unit conversion errors. Final Answer: 4 months

Question 20

The true discount on a bill due 10 months hence at 6% per annum is Rs. 26.25. Find the amount of the bill (face value).

Accepted Answer

Introduction / Context: With true discount, we can recover the face value by inverting the TD formula using the given time and rate. Given Data / Assumptions: TD = 26.25 t = 10 months = 10/12 years r = 6% per annum Concept / Approach: TD = F * (r * t) / (1 + r * t). Solve F = TD * (1 + r * t) / (r * t). Step-by-Step Solution: t = 10/12 = 5/6; r * t = 0.06 * 5/6 = 0.05. F = 26.25 * (1 + 0.05)/0.05 = 26.25 * 1.05 / 0.05 = 26.25 * 21 = 551.25. Verification / Alternative check: Present worth P = F/(1 + 0.05) = 551.25/1.05 = 525; TD = 551.25 − 525 = 26.25, consistent. Why Other Options Are Wrong: 550.00, 551.50, 550.25 do not yield TD = 26.25 when substituted into the formula. Common Pitfalls: Not converting months to years; mixing TD with SI on face value. Final Answer: Rs. 551.25

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