Welcome to Westonci.ca, the place where your questions are answered by a community of knowledgeable contributors. Our platform provides a seamless experience for finding precise answers from a network of experienced professionals. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.
Sagot :
To determine how much you will have in the account at the beginning of the 7th year with a simple interest rate of [tex]\(2\%\)[/tex] per year, we can follow these steps:
1. Identify the variables in the given formula:
- Principal ([tex]\(P\)[/tex]): \[tex]$4500 (initial deposit) - Annual interest rate (\(r\)): 0.02 (2%) - Number of years (\(n\)): 7 2. Insert these values into the equation: \[ A(n) = 4500 + (n-1)(0.02 \cdot 4500) \] 3. Substitute \(n\) with 7: \[ A(7) = 4500 + (7-1)(0.02 \cdot 4500) \] 4. Simplify inside the parentheses: \[ A(7) = 4500 + 6(0.02 \cdot 4500) \] 5. Calculate the interest amount for one year: \[ 0.02 \cdot 4500 = 90 \] 6. Multiply this interest amount by the number of years minus one (since interest compounds on the initial amount): \[ 6 \cdot 90 = 540 \] 7. Add the interest obtained over 6 years to the principal amount: \[ A(7) = 4500 + 540 = 5040 \] 8. Round the result to the nearest dollar if necessary (in this case, it remains the same): \[ A(7) = 5040 \] Therefore, at the beginning of the 7th year, you will have \$[/tex]5040 in the account.
So, the correct answer is A. \$5040.
1. Identify the variables in the given formula:
- Principal ([tex]\(P\)[/tex]): \[tex]$4500 (initial deposit) - Annual interest rate (\(r\)): 0.02 (2%) - Number of years (\(n\)): 7 2. Insert these values into the equation: \[ A(n) = 4500 + (n-1)(0.02 \cdot 4500) \] 3. Substitute \(n\) with 7: \[ A(7) = 4500 + (7-1)(0.02 \cdot 4500) \] 4. Simplify inside the parentheses: \[ A(7) = 4500 + 6(0.02 \cdot 4500) \] 5. Calculate the interest amount for one year: \[ 0.02 \cdot 4500 = 90 \] 6. Multiply this interest amount by the number of years minus one (since interest compounds on the initial amount): \[ 6 \cdot 90 = 540 \] 7. Add the interest obtained over 6 years to the principal amount: \[ A(7) = 4500 + 540 = 5040 \] 8. Round the result to the nearest dollar if necessary (in this case, it remains the same): \[ A(7) = 5040 \] Therefore, at the beginning of the 7th year, you will have \$[/tex]5040 in the account.
So, the correct answer is A. \$5040.
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.