Question

question 10 (mandatory) (1 point)
$200 is invested at 4% per year compounded semi - annually. the amount obtained after 5 years is
a) $244.04
b) $240.00
c) $243.33
d) $243.80

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.
Given $P=\$200$, $r = 0.04$, $n = 2$ (semi - annual compounding), and $t = 5$.

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 $(1.02)^{10}$

$(1.02)^{10}\approx1.218994427$.

Step4: Calculate the final amount

$A=200\times1.218994427\approx243.80$.

Answer:

d) $\$243.80$