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).
Important Questions from Compound Interest
At what rate percent per annum will Rs. 7200 amount to Rs. 7938 in one year, if interest is compounded half yearly?
What is the compound interest (in Rs.) on a sum of Rs. 8192 for \(1 \frac{1}{4}\) years at 15% per annum, if interest is compounded 5-monthly ?
What is the difference (in Rs.) between the interests on Rs. 50,000 for one year at 8% per annum compounded half yearly and yearly?
A sum of money becomes Rs. 11,880 after 4 years and Rs. 17,820 after 6 years on compound interest, if the interest is compounded annually. What is the half of the sum (in Rs.)?
A sum invested at compound interest amounts to Rs. 7,800 in 3 years and Rs. 11,232 in 5 years. What is the rate per cent?
