To calculate the total amount in the account after 5 years with an interest rate of 7% compounded semi-annually, 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 deposit).
- \( r \) 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)
- \( r = 0.07 \) (annual interest rate of 7%)
- \( n = 2 \) (compounded semi-annually)
- \( t = 5 \) (invested for 5 years)
Now, we can substitute these values into the formula:
\[ A = 100 \left(1 + \frac{0.07}{2}\right)^{2 \cdot 5} \]
Calculating the values step-by-step:
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Calculate \( \frac{r}{n} \): \[ \frac{0.07}{2} = 0.035 \]
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Calculate \( nt \): \[ 2 \cdot 5 = 10 \]
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Substitute these values into the formula: \[ A = 100 \left(1 + 0.035\right)^{10} \] \[ A = 100 \left(1.035\right)^{10} \]
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Calculate \( (1.035)^{10} \): \[ (1.035)^{10} \approx 1.4107 \]
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Finally, calculate \( A \): \[ A \approx 100 \times 1.4107 \approx 141.07 \]
Rounded to the nearest dollar, the total amount in the account after 5 years will be:
\[ \boxed{141} \]