Compound Interest Calculation: Solved Examples and Detailed Explanations

In the world of finance, understanding compound interest is crucial for managing and improving one's financial health. This article aims to provide a step-by-step explanation of how to calculate the sum of money given the amount after a certain period. We will explore the methodology using a practical example while addressing common misconceptions.

Common Misconceptions in Compound Interest Calculations

Question: A sum of money becomes 26500 after 3 years and 10562.50 after 6 years on compound interest. What is the sum?

Solution: At first glance, this question might seem legitimate, but upon closer inspection, it reveals inconsistencies. In financial mathematics, the amount increases over time due to compound interest, and it is impossible for the amount to decrease from 26500 to 10562.50 over a period of 3 years without unusual circumstances such as repeated withdrawals or penalty fees. Therefore, such a question is fundamentally flawed.

The correct approach to such problems involves a logical sequence of steps, as demonstrated in corrected examples below.

Corrected Example 1: Calculating the Principal

Scenario: An amount of money in a financial institution grows to a certain amount after a specific time period.

Given: The amount after 6 years is 10562.50, and the amount after 3 years is 26500.

Objective: Find the initial sum of money.

Step 1: Define Variables

Let the principal be P. Let the rate of interest be R. Let the amount after 3 years be X. Let the amount after 6 years be Y.

Using the compound interest formula, A P(1 R/100)^n, we can represent the given amounts.

Step 2: Form Equations

Amount after 6 years: Y P(1 R/100)^6

Amount after 3 years: X P(1 R/100)^3

Dividing Y by X:

Y/X (1 R/100)^3

Solving for R:

(10562.50/26500)^1/3 (1 R/100)

1 R/100 1.175

R/100 0.175

R 17.5%

Step 3: Calculate the Principal P

Using the value of R in the equation for X:

26500 P(1 17.5/100)^3

26500 P * 1.175^3

P 26500 / 1.175^3

P 4000

Conclusion: The initial sum of money is Rs. 4000.

Corrected Example 2: Another Scenario

Scenario: Another example with slightly different numbers.

Given: 6690 is the amount after 3 years, and 10035 is the amount after 6 years.

Step 1: Define Variables

Let the principal be A. Let the rate of interest be R.

Using the compound interest formula again:

Amount after 6 years: 10035 A(1 R/100)^6

Amount after 3 years: 6690 A(1 R/100)^3

Dividing the second equation by the first:

(10035 / 6690)^(1/3) 1 R/100

1 R/100 1.5

R/100 0.5

R 50%

Step 2: Calculate the Principal A

Using the value of R in the equation for 6690:

6690 A(1 50/100)^3

6690 A * 1.5^3

A 6690 / 1.5^3

A 4460

Conclusion: The initial amount is Rs. 4460.

Conclusion

In financial mathematics, it is essential to ensure the logical consistency of the problem. Questions should reflect a realistic and plausible scenario. When solving compound interest problems, it is crucial to follow a step-by-step approach and use the compound interest formula to accurately determine the principal or rate of interest. By doing so, one can avoid common misconceptions and achieve the correct solution.

Keywords: compound interest, amount calculation, financial mathematics