Question

question 11 (mandatory) (1 point) $200 is invested at 4% per year compounded semi - annually. the amount obtained after 5 years is
a) $243.33
b) $244.04
c) $243.80
d) $240.00

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, $P=\$200$, $r = 0.04$ (since $4\%=0.04$), $n = 2$ (compounded semi - annually), and $t = 5$ years.

Step2: Substitute values into formula

$A=200(1 +\frac{0.04}{2})^{2\times5}$.
First, calculate the value inside the parentheses: $\frac{0.04}{2}=0.02$, and $1 + 0.02=1.02$.
Then, calculate the exponent: $2\times5 = 10$.
So, $A = 200\times(1.02)^{10}$.

Step3: Calculate $(1.02)^{10}$

Using a calculator, $(1.02)^{10}\approx1.21899442$.

Step4: Calculate $A$

$A=200\times1.21899442=\$243.798884\approx\$243.80$.

Answer:

c) $\$243.80$