$A=5600 \times\left(1+\frac{2.75}{100}\right)^{30}$
Answer (2)
Calculate the interest factor: 1 + \t 100 2.75 = 1.0275 .
Raise the interest factor to the power of 30: ( 1.0275 ) 30 \t ≈ 2.2566 .
Multiply by the initial investment: 5600 × 2.2566 \t ≈ 12636.97 .
The final value of A is: 12636.97 .
Explanation
Understanding the Formula We are given the formula A=5600 \times\tleft(1+\frac{2.75}{100}\right)^{30} and we need to calculate the value of A. This formula represents the future value of an investment of $5600 at an interest rate of 2.75% per period, compounded over 30 periods.
Calculating the Interest Factor First, we need to calculate the value inside the parenthesis: 1 + 100 2.75 = 1 + 0.0275 = 1.0275
Calculating the Power Next, we raise this result to the power of 30: ( 1.0275 ) 30 ≈ 2.256601728
Calculating the Final Value Finally, we multiply this by 5600: 5600 × 2.256601728 ≈ 12636.969678971998
Examples
This type of calculation is commonly used in finance to determine the future value of an investment with compound interest. For example, if you invest $5600 in a savings account that pays 2.75% interest compounded annually, after 30 years, your investment would grow to approximately $12636.97. Understanding compound interest is crucial for making informed financial decisions, whether it's saving for retirement, investing in stocks, or taking out a loan.
By calculating the interest factor and applying it over 30 years, the future value of an investment of $5600 at an interest rate of 2.75% is approximately $12636.97. This process demonstrates the concept of compound interest. It is essential for understanding personal finance decisions.
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