A principal $7000, rate 5%=0.05, and time 2 years is given.
It is stated that it is compounded semiannually, that is, twice in a year.
The question requires that you calculate the amount in the account after 2 years and the interest earned.
The formula for the amount (compound interest) is given as:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where,
• A is the final amount.
,• P is the principal
,• r is the rate
,• n is the number of times interest is compounded annually.
,• t is the time in years.
In this case P=7000, r=0.05, n=2, t=2. Substitute these values into the formula:
[tex]\begin{gathered} A=7000(1+\frac{0.05}{2})^{2(2)}=7000(1+0.025)^4 \\ =7000(1.025)^4\approx7000(1.103813) \\ \approx\$7,726.69 \end{gathered}[/tex]The equation that relates the amount, A, principal, P, and interest earned, I is given as:
[tex]A=P+I[/tex]Substitute A=7,726.69, P=7000 into the formula:
[tex]\begin{gathered} 7,726.69=7,000+I \\ \Rightarrow I=7,726.69-7,000=\$726.69 \end{gathered}[/tex]It follows that:
The amount of money in the account after 2 years is about $7,726.69.
The amount of interest earned is about $726.69.
