Question

The compound interest on Rs. 10000 at \(20 \%\) p.a. in 4 years : (a) 10736 (b) 736 (c) 20736 (d) 7280

Short answer

Answer: (a) 10736

Step-by-step solution

Write down the given values

We are given: - Principal amount (P) = Rs. 10000 - Interest rate (r) = 20% p.a. - Number of years (n) = 4

Plug the values into the compound interest formula

Now, we will apply the formula to find the total amount after 4 years: \(A = P(1 + \frac{r}{100})^n\) Replacing the values, we get: \(A = 10000(1 + \frac{20}{100})^4\)

Solve the expression

Let's solve the expression step by step: \(A = 10000(1 + \frac{20}{100})^4\) \(A = 10000(1 + 0.20)^4\) \(A = 10000(1.20)^4\) \(A = 10000(2.0736)\) \(A = 20736\)

Find the compound interest

The compound interest is the difference between the total amount (A) and the principal amount (P). So, we have: Compound Interest = A - P Compound Interest = 20736 - 10000 Compound Interest = 10736 Comparing the obtained compound interest value with the given options, we see that it matches with option (a). Therefore, the correct answer is (a) 10736.

Key concepts

Interest Calculation

Interest calculation is a fundamental concept in financial mathematics. It's the amount charged on top of the principal, or initial amount of money, over a specified period. There are two main types:

• Simple Interest: This is calculated on the principal amount only, using the formula \(I = \frac{P \times r \times n}{100}\), where \(I\) is the interest, \(P\) is the principal, \(r\) is the rate of interest, and \(n\) is the time period.
• Compound Interest: This is calculated on the principal and also on the interest earned previously. It's better for growing investments over time.

In our exercise, we're calculating compound interest, which significantly boosts growth, especially over longer periods.
Understanding how to calculate interest is crucial for managing personal finances and investments effectively.

Compound Interest Formula

The compound interest formula is central to calculating how much a financial investment will grow over time. The formula is:
\[A = P \left(1 + \frac{r}{100}\right)^n\]
Where:

• \(A\) is the total amount after interest.
• \(P\) is the principal amount (initial investment).
• \(r\) is the annual interest rate (as a percentage).
• \(n\) is the number of years the money is invested or borrowed.

In our exercise, we used this formula to determine how the principal amount (Rs. 10000) grows at an interest rate of \(20\%\) over four years. By replacing the given values into the formula, we found that the total amount was Rs. 20736.
This formula shows the power of compound growth, which accelerates as time increases.

Financial Mathematics

Financial mathematics deals with concepts, such as interest and investment growth, essential for decision-making in finance. It helps individuals understand how money can grow over time and how different interest rates and investment periods affect that growth.

Key aspects include:

• Understanding different investment strategies.
• Analyzing the effects of compounding.
• Evaluating financial products.

Financial mathematics empowers individuals and organizations to plan and allocate resources efficiently. In our exercise, using financial mathematics allowed us to calculate compound interest effectively, demonstrating how a simple formula can inform investment decisions.

Percentage Increase

Percentage increase is how much a quantity grows compared to its original amount, expressed as a percentage. It's vital for understanding changes in finance and other sectors.

The formula for percentage increase is:
\[\text{Percentage Increase} = \frac{\text{New Value - Original Value}}{\text{Original Value}} \times 100\]
In our exercise, we calculated the increase in the investment of Rs. 10000 after applying compound interest. The original value increased to Rs. 20736, which means the compound interest was Rs. 10736.
This approach helps understand investment growth as a proportion of the original amount, giving a clear picture of the performance over time.