What annual instalment will discharge a debt of Rs. 4600 due in 4 years at 10% p.a. simple interest?

NORCET 7 Prelims -2024

Reasoning

Hard

Appeared in: NORCET 7 Prelims -2024

Explanation

The problem requires finding a fixed annual payment ('installment') that, when combined with the simple interest it earns over time, will equal the total debt of Rs. 4600 at the end of 4 years.
The key is to calculate the future value of each installment at the end of the 4-year period. The first installment earns interest for 3 years, the second for 2, the third for 1, and the last earns no interest.
Summing these future values (1.3x + 1.2x + 1.1x + 1.0x) gives a total of 4.6x, which must equal the total debt of Rs. 4600.
Solving the equation 4.6x = 4600 gives x = 1000. Therefore, the annual installment is Rs. 1000.

Option A: This value is too high. An installment of Rs. 1080 would lead to an overpayment of the debt once the interest on each installment is accounted for.
Option B: This value is also too high. It likely results from a calculation error, perhaps by miscalculating the total interest period or summing the coefficients incorrectly.
Option C: This value is too low. Four installments of Rs. 950 would only sum to Rs. 3800, which is less than the debt amount even before considering any interest earned by the lender.

Visual 1: Formula Card - A card displaying the formula for calculating the annual installment for a debt under simple interest: x = (100 * A) / [100n + (Rn*(n-1)/2)], with each variable clearly defined.
Visual 2: Timeline Diagram - A timeline from Year 0 to Year 4 showing when each installment (x) is paid and illustrating the duration for which each installment accrues interest.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating Annual Installment for a Debt with Simple Interest as background academic context rather than a clinical decision trigger.
What if? - If the stem changed one defining clue so that Rs.1000/- no longer matched, reassess the option whose mechanism, classification, or indication now fits the revised presentation.

How to Approach the Question

Identify the given values: Total Debt (A) = Rs. 4600, Time (n) = 4 years, and Rate (R) = 10% simple interest.
Understand the goal: Find the equal annual installment (let's call it 'x'). The sum of these installments plus the interest they earn must equal the total debt at the end of the term.
Recall or derive the logic: The first payment earns interest for (n-1) years, the second for (n-2) years, and so on, until the last payment which earns no interest.
Set up the equation: x + (x + xR1/100) + (x + xR2/100) + ... + (x + xR(n-1)/100) = Debt.
For this problem: x + (x + 0.1x) + (x + 0.2x) + (x + 0.3x) = 4600. This simplifies to 4.6x = 4600.
Alternatively, use the direct formula: x = (100 * A) / [100n + (Rn*(n-1)/2)].

Concept Tested & Keywords

Concept Tested: Calculating Annual Installment for a Debt with Simple Interest
Stem keywords: annual instalment, debt, Rs. 4600, 4 years, 10% p.a., simple interest
Lead-in keywords: What

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