Solving Compound Interest Problems: A Step-by-Step Guide

Understanding compound interest is crucial for financial planning and investment decisions. In this guide, we will walk you through the process of solving a specific compound interest problem, using a real-world scenario involving the growth of an initial sum over three years.

Problem Overview

A sum of Rs. 3212 grows to Rs. 3419.63 over a period of 3 years. To find the rate of compound interest that makes this growth possible, we will use the compound interest formula and break down the steps involved.

Compound Interest Formula

The compound interest formula is given by:

Amount P1r/100^t

Where:

P Principal amount (Rs. 3212)

r Rate of interest per year (which we need to find)

t Time in years (3 years)

Amount Rs. 3419.63

Plugging in the known values, we get:

Setting Up the Equation

Amount P(1 r/100)^t

3419.63 3212(1 r/100)^3

(1 r/100)^3 3419.63/3212

Solving for r

(1 r/100)^3 1.0646

1 r/100 1.021

r/100 0.021

r 2.1%

Therefore, the rate of compound interest is approximately 2.1%.

Beyond the Basics

For more complex scenarios, the equation can be solved using logarithms. The advanced equation is:

3419.63 3212(1 r/100)^3

(1 r/100)^3 3419.63/3212 1.0646

1 r/100 1.021

r/100 0.021

r 2.1%

By taking the cube root within the logarithm:

log(1 r/100) (log(1.0646))/3

0.021

This reinforces that the interest rate is 2.1%.

Conclusion

Solving compound interest problems involves setting up and solving an equation using the given principal, amount, and time. The result provides valuable insights into the rate of growth of investments over time. Understanding these calculations helps in making informed financial decisions and optimizing investment growth rates.

Additional Resources

Investopedia - Compound Interest

Financial Basics - Compound Interest

Loan Calculators