The amount in account after 7 years is $ 5499.445
Solution:
The formula for total amount in compound interest is given as:
[tex]A = p(1+\frac{r}{n})^{nt}[/tex]
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per unit t
t = the time the money is invested or borrowed for
Here given that,
A = ?
P = 4000
t = 7 years
[tex]r = 4.6 \% = \frac{4.6}{100} = 0.046[/tex]
n = 2 ( since compounded semi annually)
Substituting the values in formula, we get
[tex]A = 4000(1+\frac{0.046}{2})^{2 \times 7}\\\\Simplify\ the\ above\ expression\\\\A = 4000(1+0.023)^{14}\\\\A = 4000(1.023)^{14}\\\\A = 4000 \times 1.37486\\\\A = 5499.445[/tex]
Thus amount in account after 7 years is $ 5499.445
