#### Explanation:

For this type of question, we would use Compound Interest which is gaining interest continuously over a certain amount of years, instead of working them all out separately. The formula for Compound Interest is:

$A = P {\left(1 + r / n \times 100\right)}^{t}$

Where $A$ is the amount of interest, $P$ is the original amount, $R$ is the interest rate, $N$ is how many times interested per year and $T$ is the time.

Plugging in values:

A=$800(1+5.3/200)^8 We change this to $^ 8$as semiannually means twice a year, and as this is after $4$years, we double it to get $8.$Plugging into calculator: =$986.1923212

Rounding to 2 d.p:

$986.19 Minusing the before value from the after value: $986.19-800=$186.19 Feb 28, 2018 Rounding to 2 decimal places gives $186.18 being owed in interest

#### Explanation:

$\textcolor{b l u e}{\text{Some thoughts}}$

Note that 'semiannually' means twice per year. So each year has 2 calculation cycles

You have to 'split up' the annual percentage into a proportion that reflects the calculation cycle.

So the annual interest of 5.3% becomes 5.3/2% at each calculation cycle.

The general form for this context is

$\textcolor{w h i t e}{\text{dddddddd}} P {\left(1 + \frac{x}{2 \times 100}\right)}^{2 n}$

where $x = 5.3$ and $n$ is the count in years
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$\textcolor{b l u e}{\text{Answering the question}}$

P(1+x/(2xx100))^(2n)color(white)("ddd")->color(white)("ddd")$800(1+5.3/(2xx100))^(2xx4) color(white)("dddddddddddddddddd")->color(white)("ddd")$800(205.3/200)^8 ~~986.1923...

The amount owed is
$986.1923... ul($800.0000 larr" Subtract")
$186.1923... Rounding to 2 decimal places gives $186.18 being owed in interest