A certain sum amounts to ₹14,641 in 4 years at an annual compound interest rate of 10%. What will be the amount of the same sum at the same rate for 2½ years?

Appeared in: JSSH Staff Nurse - 2019

Explanation

The problem requires a two-step calculation: first finding the principal and then calculating the new amount for a different time period.
Using the compound interest formula A = P(1 + R/100)ᵗ, the principal (P) is calculated from the given amount (₹14,641) after 4 years at 10%. This gives P = 14,641 / (1.1)⁴ = ₹10,000.
Next, the amount for 2.5 years is calculated on this principal. The amount after 2 years is ₹10,000 * (1.1)² = ₹12,100.
For the remaining half-year, interest is calculated on the new principal of ₹12,100 at a rate of 5% (half of the annual 10% rate).
The interest for the half-year is ₹12,100 * 0.05 = ₹605.
The final amount is the sum of the amount after 2 years and the interest for the last half-year: ₹12,100 + ₹605 = ₹12,705.

Option A: This is the amount calculated for only 2 years, completely ignoring the interest for the additional half-year.
Option C: This value likely results from a calculation error, possibly by incorrectly applying simple interest or miscalculating the interest for the final half-year.
Option D: This is the amount calculated for 3 full years, not 2.5 years.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Compound Interest Calculation as background academic context rather than a clinical decision trigger.
This question tests basic numeracy and problem-solving skills, which are fundamental for various calculations in professional settings, including those outside of healthcare.
Understanding percentage and interest calculations is a foundational mathematical skill applicable to personal finance and economic literacy.
What if the interest was compounded semi-annually instead of annually? The entire calculation would change. The rate per period would be 5% and the number of periods would be 8 for the first part, and 5 for the second part, leading to a different principal and final amount.

How to Approach the Question

First, identify all the given information in the problem: the final amount (₹14,641), the time period (4 years), and the compound interest rate (10% per annum).
Recognize that the principal amount is missing. Your first goal is to calculate this principal.
Use the standard formula for compound amount: A = P(1 + R/100)ᵗ. Rearrange it to solve for P: P = A / (1 + R/100)ᵗ.
Substitute the given values to find the principal: P = 14,641 / (1 + 10/100)⁴.
Once the principal is found, use it to calculate the new amount for the required time of 2.5 years.
For a fractional time period like 2.5 years, calculate the compound amount for the whole number of years (2) first. Then, calculate the simple interest for the fractional part (0.5 year) on the amount accumulated after 2 years.

Concept Tested & Keywords

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