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Andy has $150 in a savings account that earns a simple interest rate of 5%. How much will be in Andy's savings account after 3 years?choicesA. $172.50B. $22.50C. $1,725.00D. $2,250.00

User Jaxoncreed
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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:


\textcolor{#FF7968}{P}\text{\textcolor{#FF7968}{ = \$150}}

As per her contract her savings are to receive a Simple Interest Rate ( R ) annually of:


\textcolor{#FF7968}{R}\text{\textcolor{#FF7968}{ = 5\%}}

The time frame ( t ) over which the accumulated amount is to be determined is as follows:


\textcolor{#FF7968}{t}\text{\textcolor{#FF7968}{ = 3 years}}

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:


\textcolor{#FF7968}{I}\text{\textcolor{#FF7968}{ = }}\textcolor{#FF7968}{(P\cdot R\cdot t)/(100)}

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:


\begin{gathered} I\text{ =}(150\cdot5\cdot3)/(100) \\ \\ I\text{ = }(2250)/(100) \\ \\ \textcolor{#FF7968}{I}\text{\textcolor{#FF7968}{ = \$22.5}} \end{gathered}

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:


\text{Total amount at end of 3 years = Principal saved ( P ) + Simple interest ( I )}

Go ahead and plug in the respective results in the expression above as follows:


\begin{gathered} \text{Total amount in savingd account = \$150 + \$22.5} \\ \text{\textcolor{#FF7968}{Total amount in savingd account = \$172.5}} \end{gathered}

Hence, the amount in Andy's account after 3 years would be:


\text{\textcolor{#FF7968}{Option A...\$172.5}}

User Fcat
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