Question

Ken’s sister borrowed $530 from the bank at 8.4% per year.

A) how much interest did she pay in one year
b) how much interest did she pay in three years

Answer 1

`~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$530\\ r=rate\to 8.4\%\to (8.4)/(100)\dotfill &0.084\\ t=years\dotfill &1 \end{cases} \\\\\\ I=(530)(0.084)(1)\implies I=44.52 \\\\[-0.35em] \rule{34em}{0.25pt}`

`~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$530\\ r=rate\to 8.4\%\to (8.4)/(100)\dotfill &0.084\\ t=years\dotfill &3 \end{cases} \\\\\\ I=(530)(0.084)(3)\implies I=133.56`

Answer 2

A) She pays $44.52 in one year.

B) She pays $133.56 in three years.

Step-by-step Step-by-step explanation:

Ken’s sister borrowed $530 from the bank at 8.4% per year.

A) how much interest did she pay in one year

Here's the required formula to find the interest :

`\longrightarrow{\tt{I = (PRT)/(100)}}`

• 
  `\purple\star` P = Principle
• 
  `\purple\star` R = Rate
• 
  `\purple\star` T = Time

Substituting all the given values in the formula to find the interest for one year :

`\begin{gathered} \qquad\longrightarrow{\sf{I = (PRT)/(100)}} \\ \\ \qquad\longrightarrow{\sf{I = (P * R * T)/(100)}} \\ \\ \qquad\longrightarrow{\sf{I = (530 * 8.4 * 1)/(100)}} \\ \\ \qquad\longrightarrow{\sf{I = (530 * 8.4)/(100)}} \\ \\ \qquad\longrightarrow{\sf{I = (4452)/(100)}} \\ \\ \qquad\longrightarrow{\sf{\underline{\underline{\red{I = \$44.52}}}}} \end{gathered}`

Hence, the interest is $44.52.

`\begin{gathered}\end{gathered}`

b) how much interest did she pay in three years

Here's the required formula to find the interest :

`\longrightarrow{\tt{I = (PRT)/(100)}}`

• 
  `\pink\star` P = Principle
• 
  `\pink\star` R = Rate
• 
  `\pink\star` T = Time

Substituting all the given values in the formula to find the interest for three years :

`\begin{gathered} \qquad\longrightarrow{\sf{I = (PRT)/(100)}} \\ \\ \qquad\longrightarrow{\sf{I = (P * R * T)/(100)}} \\ \\ \qquad\longrightarrow{\sf{I = (530 * 8.4 * 3)/(100)}} \\ \\ \qquad\longrightarrow{\sf{I = (530 * 25.2)/(100)}} \\ \\ \qquad\longrightarrow{\sf{I = (13356)/(100)}} \\ \\ \qquad\longrightarrow{\sf{\underline{\underline{\red{I = \$133.56}}}}} \end{gathered}`

Hence, the interest is $133.56.

`\rule{300}{2.5}`