Question

You have 2 different savings accounts. For Account A, the simple interest earned after 3months is $0.95. For Account B, the simple interest earned after 15 months is $21.00. If the interestrate is 3.8% for Account A and 2.4% for Account B, how much is the principal in each account? Whichaccount earned you the most interest the first month? Explain your answer.Account A has a principal of $).

Answer 1

• Account A has a principal of $100

,

• Account B has a principal of $700

,

• Account B earned you the most interest in the first month.

Step-by-step explanation:

Account A

• Simple Interest = $0.95

,

• Time = 3 months = 3/12 years

,

• Interest Rate=3.8%

We know that:

`\begin{gathered} $Simple\: Interest=(Principal X Rate X Time)/(100)$ \\ 0.95=(P*3.8*(3)/(12))/(100) \\ P*3.8*(3)/(12)=95 \\ 0.95P=95 \\ P=(95)/(0.95) \\ P=\$100 \end{gathered}`

Account B

• Simple Interest = $21

,

• Time = 15 months = 15/12 years

,

• Interest Rate=2.4%

We know that:

`\begin{gathered} $Simple\: Interest=(Principal X Rate X Time)/(100)$ \\ 21=(P*2.4*(15)/(12))/(100) \\ P*2.4*(15)/(12)=2100 \\ 3P=2100 \\ P=(2100)/(3) \\ P=\$700 \end{gathered}`

Next, we determine the account that earned you the most interest in the first month.

Account A (Interest in the First Month)

`\begin{gathered} $Simple\: Interest=(Principal X Rate X Time)/(100)$ \\ =(100*3.8*(1)/(12))/(100) \\ =\$0.32 \end{gathered}`

Account B (Interest in the First Month)

`\begin{gathered} $Simple\: Interest=(Principal X Rate X Time)/(100)$ \\ =(700*2.4*(1)/(12))/(100) \\ =\$1.40 \end{gathered}`

We see that Account B earned you the most interest in the first month.