Calculating interest on an annual compound basis, after how many years will the compound interest on an amount of ₹700 at an annual rate of 10% be ₹147?

1. A

   3 years

2. B

   1 year

3. C

   4 years

4. D

   2 years

Appeared in: NHM UP Staff Nurse-2023 shift 1st

Explanation

• The core of this problem is finding the time period (n) using the compound interest formula: A = P(1 + R/100)ⁿ.
• First, calculate the total amount (A) by adding the principal (P = ₹700) and the compound interest (CI = ₹147), which gives A = ₹847.
• Substitute the known values into the formula: 847 = 700(1 + 10/100)ⁿ.
• Simplify the equation: 847/700 = (1.1)ⁿ, which results in 1.21 = (1.1)ⁿ.
• Recognize that 1.21 is the square of 1.1, so (1.1)² = (1.1)ⁿ.
• By comparing the exponents, we find that n = 2 years.

Why Other Options Were Wrong

• Option A: After 3 years, the total amount would be 700 × (1.1)³ = ₹931.7. The compound interest would be 931.7 - 700 = ₹231.7, which is not ₹147.
• Option B: After 1 year, the interest would be 10% of ₹700, which is ₹70. This is simple interest, not the compound interest of ₹147.
• Option C: After 4 years, the total amount would be 700 × (1.1)⁴ = ₹1024.87. The compound interest would be 1024.87 - 700 = ₹324.87, which is much higher than ₹147.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating the time period in a compound interest problem 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, such as savings, investments, and loans.
• This concept helps in making informed decisions about long-term financial goals, like retirement planning or saving for a major purchase.
• What if the interest was simple instead of compound? The interest would be ₹70 each year. To earn ₹147 in simple interest, it would take 147 / 70 = 2.1 years.

How to Approach the Question

• First, identify all the given values in the problem: Principal (P), Rate (R), and Compound Interest (CI).
• Determine the unknown variable you need to find, which is the time period (n).
• Recall the formula for compound interest: A = P(1 + R/100)ⁿ. Remember that Amount (A) = Principal (P) + Interest (CI).
• Calculate the total amount (A) using the given P and CI.
• Substitute all known values into the formula.
• Solve the resulting equation for 'n'. This may involve simplifying fractions and recognizing powers of numbers.

Concept Tested & Keywords

• Concept Tested: Calculating the time period in a compound interest problem.
• Stem keywords: compound interest, ₹700, 10%, ₹147
• Lead-in keywords: after how many years

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qV2LXaLscOx4E-7VPvzAv

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