AIIMS Rishikesh & Jod…: What annual instalment will discharge a debt of Rs. 4600 due in 4 years at 10% p.a. simple interest?

AIIMS Rishikesh & Jodhpur NO - 2017

Quantitative Aptitude and Mathematics

Hard

Appeared in: AIIMS Rishikesh & Jodhpur NO - 2017

Explanation

The problem is about finding an equal annual installment to clear a debt, considering that each installment paid earns simple interest for the time remaining until the final due date.
The total debt of Rs. 4600 represents the future value that must be accumulated by the sum of all installments and the interest they earn.
Let the installment be 'x'. The first installment earns interest for 3 years, the second for 2, the third for 1, and the last for 0 years.
The sum of the future values of these installments is 1.3x + 1.2x + 1.1x + 1.0x = 4.6x.
Equating this to the total debt, 4.6x = 4600, and solving for x gives the installment amount as Rs. 1000.

Option B: If the annual installment were Rs. 950, the total amount paid and accumulated at the end of 4 years would be 4.6 * 950 = Rs. 4370. This amount is insufficient to clear the debt of Rs. 4600.
Option C: If the annual installment were Rs. 1050, the total amount paid and accumulated at the end of 4 years would be 4.6 * 1050 = Rs. 4830. This amount is more than the required debt of Rs. 4600.
Option D: If the annual installment were Rs. 1080, the total amount paid and accumulated at the end of 4 years would be 4.6 * 1080 = Rs. 4968. This amount is significantly higher than the debt of Rs. 4600.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating Annual Installments with Simple Interest as background academic context rather than a clinical decision trigger.
Understanding loan and interest calculations is a crucial life skill for financial literacy, helping in managing personal finances, loans, and investments.
This type of calculation is fundamental to financial products like equated monthly installments (EMIs), although EMIs typically use compound interest, which is a more complex calculation.
What if? If the interest were compounded annually instead of simple interest, the calculation would involve a geometric series. The required installment would be slightly lower because interest would also be earned on previously accrued interest, making the investment grow faster.

How to Approach the Question

First, identify the key parameters from the question: Total Debt (A = 4600), Time period (n = 4 years), and Rate of Simple Interest (R = 10%).
Recognize that this is an 'equal installments' problem where each payment earns interest for the remaining duration of the loan term.
Let the unknown annual installment be 'x'.
Calculate the future value of each installment at the end of the 4-year period. The first installment (paid after year 1) will have 3 years to earn interest, the second will have 2 years, and so on.
Sum the future values of all four installments. This sum must be equal to the total debt that needs to be discharged.
Formulate the equation: (x + SI for 3 yrs) + (x + SI for 2 yrs) + (x + SI for 1 yr) + x = 4600.

Concept Tested & Keywords

Concept Tested: Calculating Annual Installments 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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