X invested an amount of Rs. 15,000 in a fixed deposit for 2 years at compound interest rate of 5 percent p.a. How much amount will he receive at maturity?

1. A

   Rs. 16,537.5

2. B

   Rs. 16,500

3. C

   Rs. 17,265.5

4. D

   Rs. 15,750

Appeared in: DSSSB - 29 August 2019 (Shift-2)

Explanation

• The correct formula for annual compound interest is A = P(1 + r)ⁿ, where A is the final amount, P is the principal, r is the annual rate, and n is the number of years.
• Given P = 15,000, r = 5% (or 0.05), and n = 2 years.
• Substituting the values: A = 15,000 × (1 + 0.05)².
• Calculating the expression: A = 15,000 × (1.05)² = 15,000 × 1.1025.
• The final amount is Rs. 16,537.5.

Why Other Options Were Wrong

• Option B: This is the result of calculating simple interest [A = P(1 + rt)], not compound interest. It fails to account for interest being earned on the accumulated interest from the first year.
• Option C: This amount is mathematically incorrect for the given principal, rate, and time period. It does not align with either simple or compound interest formulas.
• Option D: This amount represents the total after only one year of simple interest (15,000 + (15,000 * 0.05 * 1) = 15,750). It ignores the second year of the investment period.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculation of Compound Interest as background academic context rather than a clinical decision trigger.
• Understanding compound interest is a fundamental aspect of financial literacy, crucial for personal financial planning, including savings, investments, and loans.
• This concept helps in making informed decisions about long-term financial goals, such as retirement planning or saving for a major purchase.
• What if the interest was compounded semi-annually? The formula would change to A = P(1 + r/2)^(2*n). The final amount would be slightly higher (Rs. 16,543.14) because interest is calculated more frequently.

How to Approach the Question

• First, identify the type of interest mentioned in the question (simple or compound). Here, it is 'compound interest'.
• Recall the correct formula for annual compound interest: A = P(1 + r)ⁿ.
• Carefully extract all the given values from the problem: Principal (P), rate (r), and time (n).
• Convert the percentage rate into a decimal by dividing by 100.
• Substitute these values into the formula and perform the calculation step-by-step to avoid errors.
• Compare your final calculated amount with the given options to find the correct answer.

Concept Tested & Keywords

• Concept Tested: Calculation of Compound Interest
• Stem keywords: invested, Rs. 15,000, fixed deposit, 2 years, compound interest, 5 percent p.a.
• Lead-in keywords: How much amount

Question ID

QZMyJnsS6FI9gCkPs3QA-y

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