It is given that $2000 was placed in an account that pays 16% interest compounded each year.
The Compound Interest Formula is given as:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where P is the amount placed in the account, r is the interest rate, n is the number of times the interest is compounded in a year, and t is the time passed in years.
(a) It is required to find the amount after 1 year.
Substitute P=2000, r=16%=0.16, n=1, and t=1 into the equation:
[tex]\begin{gathered} A=2000(1+\frac{0.16}{1})^{1(1)} \\ \Rightarrow A=2000(1+0.16)^1=2000(1.16)=\$2320 \end{gathered}[/tex](b) It is required to find the amount after 2 years.
Substitute P=2000, r=16%=0.16, n=1, and t=2 into the equation:
[tex]\begin{gathered} A=2000(1+\frac{0.16}{1})^{1(2)} \\ \Rightarrow A=2000(1+0.16)^2=2000(1.16)^2=2000(1.3456)=\$2691.2 \end{gathered}[/tex]Answers:
(a) $2320
(b) $2691.2
