Answer :
We will investigate the application of simple interest on any amount saved.
Lexi deposited an initial principal ( P ) amount in her saving's account. We will write down the initial savings as follows:
[tex]\textcolor{#FF7968}{P}\text{\textcolor{#FF7968}{ = \$20}}[/tex]A saving's account is a contract between the user and the bank which is signed for certain amount of interest rate ( R ). This interest rate ( R ) defines at what percentage the initially savings ( P ) will be compounded. In this simplest terms its an "extra value added" over the initial saving.
We will go ahead and express the rate ( R ) that was signed by Lexi as interest:
[tex]\textcolor{#FF7968}{R}\text{\textcolor{#FF7968}{ = 10\%}}[/tex]To determine the actual amount of simple interest earned by Lexi pertains to the time period ( t ) over which account balance is to be evaluated. This is a contractual time period given as follows:
[tex]\textcolor{#FF7968}{t}\text{\textcolor{#FF7968}{ = 3 years}}[/tex]The above three are parameters for determining the simple interest ( I ) for any initial principal amount ( P ) at an interest rate ( R ) compounded annually for a contractual time period ( t ). We can mathematically express the simple interest ( I ) as follows:
[tex]\begin{gathered} I\text{ = }\frac{P\cdot R\cdot t}{100}\text{ } \\ \textcolor{#FF7968}{I}\text{\textcolor{#FF7968}{ = P}}\textcolor{#FF7968}{\cdot r\cdot t\ldots}\text{\textcolor{#FF7968}{ Eq1}} \end{gathered}[/tex]Once we have evaluated the " extra amount " we will add this amount to Lexi's initial deposit ( P ) and determine the her account balance after the contractual period as follows:
[tex]\text{\textcolor{#FF7968}{Lexi Account Balance = Simple Interest ( I ) + P }}\textcolor{#FF7968}{\ldots}\text{\textcolor{#FF7968}{ Eq2}}[/tex]Now we will combine the two expression ( Eq1 and Eq2 ) as follows:
[tex]\begin{gathered} \text{Lexi Account Balance = P}\cdot r\cdot t\text{ + P} \\ \text{\textcolor{#FF7968}{Lexi Account Balance = P}}\textcolor{#FF7968}{\cdot(1+r\cdot t)}\text{\textcolor{#FF7968}{ }} \end{gathered}[/tex]Now we will use the above expression to determine Lexi's account balance after contractual period. We will plug in the respective quantities as follows:
[tex]\begin{gathered} \text{Lexi Account Balance = }20\cdot(\text{ 1 + }\frac{20}{100}\cdot3) \\ \\ \text{Lexi Account Balance = }20\cdot(\text{ 1.6}) \\ \text{\textcolor{#FF7968}{Lexi Account Balance = \$32 }} \end{gathered}[/tex]Therefore Lexi's account balance after 3 years is:
[tex]\textcolor{#FF7968}{32}\text{\textcolor{#FF7968}{ dollars}}[/tex]