To calculate the total amount in the account after 5 years with a 7% interest rate compounded semi-annually (two times a year), you can use the compound interest formula:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
where:
- \(A\) is the total amount after time \(t\),
- \(P\) is the principal (initial amount, in this case, $100.00),
- \(r\) is the annual interest rate (as a decimal, so 7% = 0.07),
- \(n\) is the number of times the interest is compounded per year (2 for semi-annual),
- \(t\) is the number of years the money is invested or borrowed (5 years).
Let's plug in the values:
- \(P = 100\)
- \(r = 0.07\)
- \(n = 2\)
- \(t = 5\)
Now substitute these values into the formula:
\[ A = 100 \left(1 + \frac{0.07}{2}\right)^{2 \cdot 5} \]
Calculate \( \frac{0.07}{2} \):
\[ \frac{0.07}{2} = 0.035 \]
Now substitute this back into the formula:
\[ A = 100 \left(1 + 0.035\right)^{10} \]
\[ A = 100 \left(1.035\right)^{10} \]
Now calculate \( (1.035)^{10} \):
\[ (1.035)^{10} \approx 1.4103 \]
Now multiply by the principal:
\[ A \approx 100 \cdot 1.4103 \approx 141.03 \]
Rounding to the nearest dollar gives:
\[ A \approx 141 \]
Thus, the total amount in the account after 5 years will be $141.