To calculate the total amount in an account after a specific number of years with compounded interest, we can use the formula for compound interest:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- \(A\) is the amount of money accumulated after n years, including interest.
- \(P\) is the principal amount (the initial amount of money).
- \(r\) is the annual interest rate (decimal).
- \(n\) is the number of times that interest is compounded per year.
- \(t\) is the number of years the money is invested or borrowed.
Given:
- \(P = 100\) (the initial deposit)
- \(r = 0.07\) (7% interest rate)
- \(n = 2\) (compounded twice a year)
- \(t = 5\) (the total time in years)
Let's plug in the values:
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Calculate \( \frac{r}{n} \): \[ \frac{r}{n} = \frac{0.07}{2} = 0.035 \]
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Calculate \(nt\): \[ nt = 2 \times 5 = 10 \]
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Plug the values into the formula: \[ A = 100 \left(1 + 0.035\right)^{10} \]
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Calculate \(1 + 0.035\): \[ 1 + 0.035 = 1.035 \]
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Now raise \(1.035\) to the power of \(10\): \[ 1.035^{10} \approx 1.4103 \]
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Finally, multiply by \(100\): \[ A = 100 \times 1.4103 \approx 141.03 \]
After rounding to the nearest dollar, the total amount in the account after 5 years will be:
\[ \boxed{141} \]
Triple checking:
- \(P = 100\)
- \(r = 0.07\)
- \(n = 2\)
- \(t = 5\)
Using the formula: \[ A = 100 \left(1 + 0.035\right)^{10} \] Calculating intermediate steps as before confirms: 1.035 raised to 10 gives approximately 1.4103, and multiplying gives approximately 141.03, rounding to 141.
Therefore, the final answer remains:
\[ \boxed{141} \]