What is the compound interest on a sum of ₹25,000 after three years at a rate of 12 per cent per annum interest compounded yearly?
Understanding and Calculating Compound Interest
Compound interest is a powerful concept in finance where the interest earned in each period is added to the principal amount before calculating the interest for the next period. This means you earn interest on your initial investment as well as on the accumulated interest over time.
Let's calculate the compound interest on a sum of ₹25,000 at a rate of 12 per cent per annum for three years, compounded yearly.
Given Information for Compound Interest Calculation
- Principal amount (P) = ₹25,000
- Rate of interest (r) = 12% per annum
- Time period (n) = 3 years
- Interest is compounded yearly.
Formula for Amount with Compound Interest
The formula to calculate the total amount (A) after 'n' years with compound interest compounded yearly is:
$$ A = P \left(1 + \frac{r}{100}\right)^n $$
Where:
- A = Amount after 'n' years
- P = Principal amount
- r = Annual interest rate
- n = Number of years
Step-by-Step Calculation of Amount
Let's plug in the given values into the formula:
$$ A = 25000 \left(1 + \frac{12}{100}\right)^3 $$
$$ A = 25000 \left(1 + 0.12\right)^3 $$
$$ A = 25000 \left(1.12\right)^3 $$
First, calculate $(1.12)^3$:
$$ (1.12)^3 = 1.12 \times 1.12 \times 1.12 $$
$$ (1.12)^3 = 1.2544 \times 1.12 $$
$$ (1.12)^3 = 1.404928 $$
Now, multiply this by the principal amount:
$$ A = 25000 \times 1.404928 $$
$$ A = 35123.20 $$
So, the total amount after three years is ₹35,123.20.
Calculating the Compound Interest (CI)
The compound interest is the difference between the total amount after 'n' years and the original principal amount.
$$ CI = A - P $$
Using the calculated amount and the given principal:
$$ CI = 35123.20 - 25000 $$
$$ CI = 10123.20 $$
Therefore, the compound interest on ₹25,000 after three years at a rate of 12 per cent per annum compounded yearly is ₹10,123.20.
| Calculation Step | Value |
|---|---|
| Principal (P) | ₹25,000 |
| Rate (r) | 12% |
| Time (n) | 3 years |
| $(1 + r/100)$ | $(1 + 12/100) = 1.12$ |
| $(1 + r/100)^n$ | $(1.12)^3 = 1.404928$ |
| Amount (A = P * (1 + r/100)$^n$) | $25000 \times 1.404928 = 35123.20$ |
| Compound Interest (CI = A - P) | $35123.20 - 25000 = 10123.20$ |
Revision Table: Key Formulas
| Concept | Formula (Yearly Compounding) |
|---|---|
| Amount (A) | $P \left(1 + \frac{r}{100}\right)^n$ |
| Compound Interest (CI) | $A - P$ or $P \left[\left(1 + \frac{r}{100}\right)^n - 1\right]$ |
Additional Information: Simple vs. Compound Interest
It's important to understand the difference between simple and compound interest. Simple interest is calculated only on the principal amount, whereas compound interest is calculated on the principal amount plus the accumulated interest from previous periods.
- Simple Interest: $SI = \frac{P \times R \times T}{100}$
- Compound Interest: Earns interest on interest, leading to faster growth of the investment over time.
For the same principal, rate, and time, compound interest will always be greater than or equal to simple interest (equal only when the time period is one year or less).
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