Use The Formula $A = P \left(1+\frac{r}{100}\right)^n$ To Calculate The Compound Interest At 7.5% Per Annum On A Loan Of R5,600 For 4 Years.Where:- $A$ Is The Final Amount,- $P$ Is The Principal Amount (R5,600),- $r$

Understanding Compound Interest

Compound interest is a type of interest that is calculated on both the initial principal and the accumulated interest from previous periods. It is a powerful tool for investors and lenders alike, allowing them to earn interest on their interest. In this article, we will explore how to calculate compound interest using the formula $A = P \left(1+\frac{r}{100}\right)^n$, where $A$ is the final amount, $P$ is the principal amount, $r$ is the annual interest rate, and $n$ is the number of years.

The Formula: $A = P \left(1+\frac{r}{100}\right)^n$

The formula for compound interest is a simple yet powerful tool for calculating the final amount of a loan or investment. To use the formula, you will need to know the principal amount ($P$), the annual interest rate ($r$), and the number of years ($n$). The formula is as follows:

$$A = P \left(1+\frac{r}{100}\right)^n$$

Where:

• $A$ is the final amount
• $P$ is the principal amount
• $r$ is the annual interest rate (expressed as a percentage)
• $n$ is the number of years

Calculating Compound Interest at 7.5% per Annum

Now that we have the formula, let's use it to calculate the compound interest at 7.5% per annum on a loan of R5,600 for 4 years.

• Principal amount ($P$): R5,600
• Annual interest rate ($r$): 7.5%
• Number of years ($n$): 4

Plugging these values into the formula, we get:

$$A = 5600 \left(1+\frac{7.5}{100}\right)^4$$

Simplifying the Formula

To simplify the formula, we can start by calculating the value of $\left(1+\frac{7.5}{100}\right)^4$.

$$\left(1+\frac{7.5}{100}\right)^4 = \left(1+0.075\right)^4 = 1.075^4$$

Using a calculator, we can calculate the value of $1.075^4$ as follows:

$$1.075^4 = 1.338225$$

Calculating the Final Amount

Now that we have the value of $\left(1+\frac{7.5}{100}\right)^4$, we can plug it back into the formula to calculate the final amount ($A$).

$$A = 5600 \times 1.338225 = 7501.42$$

Rounding the Final Amount

To round the final amount to the nearest cent, we can use the following calculation:

$$A = 7501.42 \approx 7501.42$$

Conclusion

In this article, we have used the formula $A = P \left(1+\frac{r}{100}\right)^n$ to calculate the compound interest at 7.5% per annum on a loan of R5,600 for 4 years. We have also simplified the formula and calculated the final amount using a calculator. The final amount is approximately R7,501.42.

Tips and Variations

• To calculate the compound interest for a different principal amount, simply plug in the new value of $P$ into the formula.
• To calculate the compound interest for a different annual interest rate, simply plug in the new value of $r$ into the formula.
• To calculate the compound interest for a different number of years, simply plug in the new value of $n$ into the formula.

Common Applications of Compound Interest

Compound interest has many practical applications in finance and economics. Some common examples include:

• Calculating the interest on a savings account or certificate of deposit (CD)
• Calculating the interest on a loan or mortgage
• Calculating the interest on an investment or retirement account
• Calculating the interest on a bond or other fixed-income security

Conclusion

$$

Understanding Compound Interest

Compound interest is a type of interest that is calculated on both the initial principal and the accumulated interest from previous periods. It is a powerful tool for investors and lenders alike, allowing them to earn interest on their interest. In this article, we will answer some of the most frequently asked questions about compound interest.

Q: What is compound interest?

A: Compound interest is a type of interest that is calculated on both the initial principal and the accumulated interest from previous periods.

Q: How is compound interest calculated?

A: Compound interest is calculated using the formula $A = P \left(1+\frac{r}{100}\right)^n$, where $A$ is the final amount, $P$ is the principal amount, $r$ is the annual interest rate, and $n$ is the number of years.

Q: What is the principal amount?

A: The principal amount is the initial amount of money that is invested or borrowed.

Q: What is the annual interest rate?

A: The annual interest rate is the rate at which interest is earned or paid on the principal amount.

Q: What is the number of years?

A: The number of years is the length of time that the interest is earned or paid.

Q: How does compound interest work?

A: Compound interest works by calculating the interest on the principal amount and then adding it to the principal amount. The interest is then calculated on the new principal amount, and so on.

Q: What are the benefits of compound interest?

A: The benefits of compound interest include:

• Earning interest on interest
• Growing wealth over time
• Increasing the value of an investment
• Reducing the amount of money needed to achieve a financial goal

Q: What are the risks of compound interest?

A: The risks of compound interest include:

• Inflation: If the interest rate is not adjusted for inflation, the purchasing power of the money may decrease over time.
• Market volatility: If the market is volatile, the value of the investment may fluctuate.
• Credit risk: If the borrower defaults on the loan, the lender may lose some or all of the principal amount.

Q: How can I use compound interest to my advantage?

A: You can use compound interest to your advantage by:

• Investing in a high-yield savings account or certificate of deposit (CD)
• Borrowing money at a low interest rate
• Investing in a diversified portfolio of stocks and bonds
• Using a compound interest calculator to determine the future value of an investment

Q: What are some common applications of compound interest?

A: Some common applications of compound interest include:

• Calculating the interest on a savings account or certificate of deposit (CD)
• Calculating the interest on a loan or mortgage
• Calculating the interest on an investment or retirement account
• Calculating the interest on a bond or other fixed-income security

Q: How can I calculate compound interest?

A: You can calculate compound interest using a compound interest calculator or by using the formula $A = P \left(1+\frac{r}{100}\right)^n$.

Q: What is the difference between compound interest and simple interest?

A: The difference between compound interest and simple interest is that compound interest is calculated on both the principal amount and the accumulated interest from previous periods, while simple interest is only calculated on the principal amount.

Conclusion

In conclusion, compound interest is a powerful tool for investors and lenders alike. By understanding how compound interest works and using it to your advantage, you can grow your wealth over time and achieve your financial goals.