Respuesta :
We will investigate the application of simple interest on any amount of savings kept in a bank.
Andy has an initial principal ( P ) amount in her saving account as follows:
[tex]\textcolor{#FF7968}{P}\text{\textcolor{#FF7968}{ = \$150}}[/tex]As per her contract her savings are to receive a Simple Interest Rate ( R ) annually of:
[tex]\textcolor{#FF7968}{R}\text{\textcolor{#FF7968}{ = 5\%}}[/tex]The time frame ( t ) over which the accumulated amount is to be determined is as follows:
[tex]\textcolor{#FF7968}{t}\text{\textcolor{#FF7968}{ = 3 years}}[/tex]To determine the amount of simple interest ( I ) accumulated at the end of the time period in consideration ( t ) as per rate ( R ) on her inital savings ( P ) can be determined from the following formula:
[tex]\textcolor{#FF7968}{I}\text{\textcolor{#FF7968}{ = }}\textcolor{#FF7968}{\frac{P\cdot R\cdot t}{100}}[/tex]The above formula calculates an " additional amount " that she would have at the end of the time period ( t ). This additional amount depends on her initial savings ( P ) and the rate of return ( R ) offered by the bank.
We will use the above formula to determine the simple interest ( additional amount ) at the end of the time period as follows:
[tex]\begin{gathered} I\text{ =}\frac{150\cdot5\cdot3}{100} \\ \\ I\text{ = }\frac{2250}{100} \\ \\ \textcolor{#FF7968}{I}\text{\textcolor{#FF7968}{ = \$22.5}} \end{gathered}[/tex]Therefore Andy's account would be further creditted by the simple interest amount ( I ) at the end of 3 years. We can add this amount into her initial principal amount saved to determine the accumulated amount at the end of 3 years that would be shown on her bank statement as follows:
[tex]\text{Total amount at end of 3 years = Principal saved ( P ) + Simple interest ( I )}[/tex]Go ahead and plug in the respective results in the expression above as follows:
[tex]\begin{gathered} \text{Total amount in savingd account = \$150 + \$22.5} \\ \text{\textcolor{#FF7968}{Total amount in savingd account = \$172.5}} \end{gathered}[/tex]Hence, the amount in Andy's account after 3 years would be:
[tex]\text{\textcolor{#FF7968}{Option A...\$172.5}}[/tex]