The amount on a sum of 15000 at 12% p.a. compounded annually for 2 years is 18,816.
Understanding Compound Interest
Compound interest is the interest calculated on the initial principal and also on the accumulated interest from previous periods on a deposit or loan. It's often referred to as "interest on interest," and it can significantly boost investment growth over time. Unlike simple interest, which is only calculated on the principal amount, compound interest allows your money to grow at an accelerating rate.
The formula for compound interest is:
A = P (1 + r/n)^(nt)
Where:
- A = the future value of the investment/loan, including interest (the amount)
- P = the principal investment amount (the initial deposit or loan amount)
- r = the annual interest rate (as a decimal)
- n = the number of times that interest is compounded per year
- t = the number of years the money is invested or borrowed for
For a deeper dive into how compound interest works, you can explore resources like Investopedia's explanation of compound interest.
Calculating the Amount
Let's apply the compound interest formula to the given problem:
- Principal Amount (P): 15,000
- Annual Interest Rate (r): 12% = 0.12
- Number of Times Compounded Per Year (n): Annually, so n = 1
- Time (t): 2 years
Here’s a breakdown of the inputs:
| Parameter | Value |
|---|---|
| Principal (P) | 15,000 |
| Annual Interest Rate (r) | 0.12 (12%) |
| Compounding Frequency (n) | 1 (annually) |
| Time in Years (t) | 2 |
| Amount (A) | 18,816 |
Now, let's perform the calculation:
-
Substitute the values into the formula:
A = 15,000 (1 + 0.12/1)^(12) -
Simplify the expression inside the parenthesis:
A = 15,000 (1 + 0.12)^2
A = 15,000 (1.12)^2 -
Calculate the exponent:
A = 15,000 * (1.2544) -
Multiply to find the final amount:
A = 18,816
Therefore, after 2 years, the total amount on the sum of 15,000 with 12% annual compounding interest will be 18,816. This amount includes both the initial principal and the accumulated interest.
Why Compound Interest Matters
- Accelerated Growth: It allows your money to grow faster because interest is earned on both the initial principal and the previously earned interest.
- Long-Term Benefits: The longer your money is invested, the more significant the effect of compounding becomes, leading to substantial returns over time.
- Financial Planning: Understanding compound interest is crucial for effective financial planning, whether for savings, investments, or loans. It highlights the importance of starting early and letting your money work for you.
