Calculating Compound Interest Rate for Rs. 100
Understanding and calculating compound interest are crucial aspects of finance. This article will guide you through the process of determining the rate of interest when the compound interest of Rs. 100 for 1 year is Rs. 15. We will also explore how compound interest differs from simple interest over time.
Compound Interest Basics
Before we begin, let us briefly review the formula for compound interest:
A P(1 r)n
A is the total amount after interest. P is the principal amount, which is the initial investment. r is the rate of interest as a decimal. n is the number of compounding periods, or the number of years.Case Study: Rs. 100 for 1 Year
Given:
The principal amount (P) is Rs. 100. The compound interest earned in 1 year is Rs. 15. The total amount after interest (A) is P 15 115. The number of years (n) is 1.We need to find the rate of interest (r).
Step-by-Step Calculation
Substitute the given values into the compound interest formula:
115 100(1 r)1
This simplifies to:
115 100(1 r)
Dividing both sides by 100:
1 r 1.15
Subtracting 1 from both sides:
r 1.15 - 1 0.15
To express the rate as a percentage, multiply by 100:
r 0.15 * 100 15%
Therefore, the rate of interest is 15%.
Difference Between Compound Interest and Simple Interest
It is important to note that for the first year, the compound interest and simple interest are the same. However, from the second year onwards, the compound interest will differ from the simple interest.
Monthly Compounding Interest
If the rate of compounding is monthly, the formula becomes:
115 100(1 r/12)12
This simplifies to:
1.15 (1 r/12)12
Dividing both sides by (1 r/12) and taking the 12th root:
1.151/12 - 1 r/12
Solving for r:
r 0.1405790030382 (or 14.06% when rounded to 2 decimal places)
Continuous Compounding Interest
If compounding is continuous, the formula is:
115 100er
This simplifies to:
1.15 er
Taking the natural logarithm (ln) of both sides:
r ln(1.15) 0.1397619423751 (or 13.98% when rounded to 2 decimal places)
Conclusion
We have determined that the rate of interest is 15% when the compound interest of Rs. 100 for 1 year is Rs. 15. Additionally, we have explored the differences between compound and simple interest for monthly and continuous compounding.