To calculate the total amount in the account after 5 years with a 7% interest rate 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 or investment).
- \( r \) 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:
- \( P = 100.00 \)
- \( r = 0.07 \) (7%)
- \( n = 2 \) (compounded twice a year)
- \( t = 5 \)
Plugging in the values:
\[ A = 100 \left(1 + \frac{0.07}{2}\right)^{2 \times 5} \]
Calculating step by step:
- Calculate \( \frac{r}{n} \):
\[ \frac{0.07}{2} = 0.035 \]
- Calculate \( nt \):
\[ 2 \times 5 = 10 \]
- Now substitute these values back into the formula:
\[ A = 100 \left(1 + 0.035\right)^{10} \]
- Calculate \( 1 + 0.035 \):
\[ 1 + 0.035 = 1.035 \]
- Now raise \( 1.035 \) to the power of 10:
\[ 1.035^{10} \approx 1.4107 \]
- Finally, multiply by the principal:
\[ A \approx 100 \times 1.4107 \approx 141.07 \]
Rounding to the nearest dollar:
\[ A \approx 141 \]
Therefore, the total amount in the account after 5 years will be approximately $141.00.