QuestionJune 17, 2025

If 7000 dollars is invested in a bank account at an interest rate of 8 per cent per year, determine each of the following. Round each answer to the nearest cent. Find the amount in the bank after 13 years if interest is compounded annually: square Find the amount in the bank after 13 years if interest is compounded quarterly: square Find the amount in the bank after 13 years if interest is compounded monthly: square Finally, find the amount in the bank after 13 years if interest is compounded continuously: square

If 7000 dollars is invested in a bank account at an interest rate of 8 per cent per year, determine each of the following. Round each answer to the nearest cent. Find the amount in the bank after 13 years if interest is compounded annually: square Find the amount in the bank after 13 years if interest is compounded quarterly: square Find the amount in the bank after 13 years if interest is compounded monthly: square Finally, find the amount in the bank after 13 years if interest is compounded continuously: square
If 7000 dollars is invested in a bank account at an interest rate of 8 per cent per year, determine each of the following. Round each answer to the nearest cent. Find the amount in the bank after 13 years if interest is compounded annually: square Find the amount in the bank after 13 years if interest is compounded quarterly: square Find the amount in the bank after 13 years if interest is compounded monthly: square Finally, find the amount in the bank after 13 years if interest is compounded continuously: square

Solution
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Answer

19,042.57 ### 19,308.96 ### 19,387.29 ### 19,442.56 Explanation 1. Calculate amount with annual compounding Use the formula for compound interest: **A = P(1 + \frac{r}{n})^{nt}**. Here, P = 7000, r = 0.08, n = 1, t = 13. Calculate A = 7000(1 + \frac{0.08}{1})^{1 \times 13}. 2. Calculate amount with quarterly compounding Use the same formula with n = 4: A = 7000(1 + \frac{0.08}{4})^{4 \times 13}. 3. Calculate amount with monthly compounding Use the same formula with n = 12: A = 7000(1 + \frac{0.08}{12})^{12 \times 13}. 4. Calculate amount with continuous compounding Use the formula for continuous compounding: **A = Pe^{rt}**. Here, P = 7000, r = 0.08, t = 13. Calculate A = 7000e^{0.08 \times 13}.

Explanation

1. Calculate amount with annual compounding<br /> Use the formula for compound interest: **$A = P(1 + \frac{r}{n})^{nt}$**. Here, $P = 7000$, $r = 0.08$, $n = 1$, $t = 13$. Calculate $A = 7000(1 + \frac{0.08}{1})^{1 \times 13}$.<br /><br />2. Calculate amount with quarterly compounding<br /> Use the same formula with $n = 4$: $A = 7000(1 + \frac{0.08}{4})^{4 \times 13}$.<br /><br />3. Calculate amount with monthly compounding<br /> Use the same formula with $n = 12$: $A = 7000(1 + \frac{0.08}{12})^{12 \times 13}$.<br /><br />4. Calculate amount with continuous compounding<br /> Use the formula for continuous compounding: **$A = Pe^{rt}$**. Here, $P = 7000$, $r = 0.08$, $t = 13$. Calculate $A = 7000e^{0.08 \times 13}$.
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