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

RRB Staff Nurse Jaipur-6th June 2018

Non Nursing Subjects

Hard

Appeared in: RRB Staff Nurse Jaipur-6th June 2018

Explanation

The problem requires finding an equal annual installment to clear a debt, considering that each installment paid earns simple interest for the remaining period.
Let the annual installment be 'x'. The total value of all installments at the end of the 4-year term must equal the debt of Rs. 4600.
The first installment (paid at end of year 1) gathers interest for 3 years. Its value becomes x + (x * 10 * 3)/100 = 1.3x.
Similarly, the values of the 2nd, 3rd, and 4th installments are 1.2x, 1.1x, and x, respectively.
The sum of these values is 1.3x + 1.2x + 1.1x + x = 4.6x.
Equating this to the total debt: 4.6x = 4600, which gives x = 1000.

Option B: An annual installment of Rs. 950 would only accumulate to a total of 4.6 * 950 = Rs. 4370 over the four years, which is insufficient to cover the Rs. 4600 debt.
Option C: An annual installment of Rs. 1050 would accumulate to a total of 4.6 * 1050 = Rs. 4830, which is more than the required amount to discharge the Rs. 4600 debt.
Option D: An annual installment of Rs. 1080 would accumulate to a total of 4.6 * 1080 = Rs. 4968, which is significantly more than the Rs. 4600 debt.

Visual 1: Flowchart: A visual flowchart illustrating the step-by-step calculation: 1. Define variables (Debt, Rate, Time). 2. Let installment be 'x'. 3. Calculate the future value of each of the four installments. 4. Sum the future values. 5. Equate the sum to the total debt. 6. Solve for 'x'.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating Annual Installments for a Debt with Simple Interest as background academic context rather than a clinical decision trigger.
Practical Relevance: Understanding how installments and interest work is a fundamental life skill for personal financial management, including managing loans (like education or housing loans), savings plans, and investments.
Financial Literacy: For nursing professionals, who often have stable but demanding careers, understanding these concepts is crucial for long-term financial planning, retirement savings, and making informed financial decisions.
What if?: If the interest was compounded annually instead of simple interest, the calculation would be more complex, involving the future value of an annuity formula, and the required installment would be different.

How to Approach the Question

Identify the question type: This is a quantitative aptitude problem involving simple interest and installments.
List the given information: Debt = Rs. 4600, Time = 4 years, Rate = 10% p.a. simple interest.
Understand the core concept: The total value of all installments, including the simple interest they earn over the remaining time, must equal the total debt.
Set up the equation: Let 'x' be the annual installment. Calculate the future value of each installment at the end of the 4-year period and sum them up.
Solve for 'x': Equate the total future value to the debt amount (4.6x = 4600) and solve for the variable 'x'.
Verify the answer: Plug the calculated installment value back into the equation to ensure it discharges the exact debt amount.

Concept Tested & Keywords

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