Introduction to Compound and Simple Interest
Interest in financial terms plays a crucial role in the accumulation of wealth over time. Two common types of interest are compound interest and simple interest. Understanding the difference between these two can be pivotal in managing finances effectively. This article provides a detailed explanation and a step-by-step approach to calculate the difference between compound interest (CI) and simple interest (SI).
Credit Calculations: Simple and Compound
Let's explore a scenario where the simple interest for 2 years is 200 at a rate of 7% per annum. We aim to find the difference between the compound interest and simple interest. The steps involved include determining the principal amount, calculating the compound interest, and then finding the difference.
Step 1: Calculating the Principal Amount
The formula for simple interest is:
SI P × r × t / 100
Where:
P Principal r Rate of interest t Time (in years)Given SI 200, r 7%, and t 2 years, we can rearrange the formula to solve for P:
P SI × 100 / (r × t)
Substituting the values:
P 200 × 100 / (7 × 2) 20000 / 14 ≈ 1428.57
Step 2: Calculating Compound Interest
The formula for compound interest is:
CI P × (1 r/100)^t - P
Substituting P 1428.57, r 7, and t 2:
1 r/100 1 7/100 1.07
(1.07)^2 1.1449
Now, calculate the compound interest:
CI 1428.57 × 1.1449 - 1428.57
1428.57 × 1.1449 ≈ 1630.77
CI 1630.77 - 1428.57 ≈ 202.20
Step 3: Calculating the Difference Between CI and SI
The difference between compound interest and simple interest is:
Difference CI - SI 202.20 - 200 2.20
Key Differences Explained
Unlike simple interest, which remains constant across each year, compound interest accumulates on the new principal amount every year. This means the interest earned in the first year is reinvested, leading to higher interest in subsequent years.
In our example, after the first year, the new principal amount becomes 107% of the initial principal. By the end of the second year, the principal increases to 114.49%. This results in a compound interest of 14.49, as compared to the simple interest of 14. Therefore, the difference is 0.49, which in terms of the principal amount is Rs.7.
Conclusion
The difference between compound interest and simple interest over a period of 2 years at a rate of 7% per annum is approximately Rs.2.20. This difference is due to the reinvestment of interest in the case of compound interest, leading to exponential growth over time.