$A=300 imes \frac{\left[\left(1+\frac{0.02}{12} ight)^{(12 \cdot 2)}-1 ight]}{\left(\frac{0.02}{12} ight)}$
$= \square$ (Round to two decimal places)

Question

$A=300 	imes \frac{\left[\left(1+\frac{0.02}{12}ight)^{(12 \cdot 2)}-1ight]}{\left(\frac{0.02}{12}ight)}$
$= \square$ (Round to two decimal places)

Anonymous · Answer

The value of A, calculated using the provided formula for compound interest, is approximately 7339.70 when rounded to two decimal places. This is achieved through a series of calculations including monthly interest adjustments and exponentiation. Understanding this formula is valuable in finance for assessing future investment values. 
 ;

GinnyAnswer · Answer

Calculate the value inside the parenthesis: 1 + " , " f r a c 0.02 12 ≈ 1.00166667 . 
 Calculate the exponent: 12" , " t im es 2 = 24 . 
 Calculate the value of ( 1 + 12 0.02 ​ ) ( 12 ⋅ 2 ) ≈ 1.04077612 . 
 Calculate A and round to two decimal places: 7339.70 ​ . 
 
 Explanation 
 
 Understanding the Problem We are given the formula: A = 300" , " t im es " , " f r a c [ ( 1 + 12 0.02 ​ ) ( 12 ⋅ 2 ) − 1 ] ( 12 0.02 ​ ) and we need to calculate the value of A and round it to two decimal places. 
 
 Calculations First, let's simplify the expression inside the parenthesis: 1 + 12 0.02 ​ = 1 + 0.001666666... ≈ 1.00166667 Next, calculate the exponent: 12 ⋅ 2 = 24 Now, we can calculate the value of the term raised to the power: ( 1 + 12 0.02 ​ ) ( 12 ⋅ 2 ) = ( 1.00166667 ) 24 ≈ 1.04077612 Subtract 1 from the result: 1.04077612 − 1 = 0.04077612 Divide the result by 12 0.02 ​ :
 12 0.02 ​ 0.04077612 ​ = 0.00166667 0.04077612 ​ ≈ 24.465672 Finally, multiply the result by 300: 300 × 24.465672 ≈ 7339.7016 Round the final result to two decimal places: 7339.7016 ≈ 7339.70 
 
 Final Answer Therefore, the value of A rounded to two decimal places is 7339.70 .

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 deposit $300 per month into an account that earns 2% annual interest compounded monthly for 2 years, this formula calculates the total amount you would have at the end of the 2 years. Understanding compound interest is crucial for making informed decisions about savings, investments, and loans.

$A=300 \times \frac{\left[\left(1+\frac{0.02}{12}\right)^{(12 \cdot 2)}-1\right]}{\left(\frac{0.02}{12}\right)}$
$= \square$ (Round to two decimal places)

Answer (2)

$A=300 \times \frac{\left[\left(1+\frac{0.02}{12}\right)^{(12 \cdot 2)}-1\right]}{\left(\frac{0.02}{12}\right)}$ $= \square$ (Round to two decimal places)

Answer (2)

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$A=300 \times \frac{\left[\left(1+\frac{0.02}{12}\right)^{(12 \cdot 2)}-1\right]}{\left(\frac{0.02}{12}\right)}$
$= \square$ (Round to two decimal places)