Question

suppose that $2000 is invested at a rate of 3.6%, compounded semiannually. assuming that no withdrawals are made, find the total amount after 4 years. do not round any intermediate computations, and round your answer to the nearest cent.

Explanation:

Step1: Identify compound - interest formula

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal), $n$ is the number of times interest is compounded per year, and $t$ is the number of years.
Here, $P=\$2000$, $r = 0.036$ (since $3.6\%=0.036$), $n = 2$ (compounded semiannually), and $t = 4$.

Step2: Substitute values into the formula

$A=2000(1 +\frac{0.036}{2})^{2\times4}=2000(1 + 0.018)^{8}$.
First, calculate inside the parentheses: $1+0.018 = 1.018$.
Then, calculate the exponent: $(1.018)^{8}\approx1.15247$.
Finally, multiply by the principal: $A = 2000\times1.15247=\$2304.94$.

Answer:

$2304.94$