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Mikayla opens a savings account with a principal balance of $3,000. After 5 years, she earns $450 in interest. Using the equation =rt , where = interest, = principal, = rate, and =time.


What is the interest rate on Mikayla’s account after 5 years?



*Note: Interest rate is given in percent form.

Respuesta :

cerverusdante
To solve this we are going to use the simple interest formula: [tex]A=P(1+rt)[/tex]
where
[tex]A[/tex] is the final amount after [tex]t[/tex] years 
[tex]P[/tex] is the initial amount 
[tex]r[/tex] is the interest rate
[tex]t[/tex] is the time in years 

We know for our problem that [tex]P=3000[/tex], and [tex]t=5[/tex]. Since she earn $450 in interest afeter 5 years, [tex]A=3000+450=3450[/tex]. Lets replace the values in our formula to find [tex]r[/tex]:
[tex]A=P(1+rt)[/tex]
[tex]3450=3000(1+5r)[/tex]
[tex]1+5r= \frac{3450}{3000} [/tex]
[tex]1+5r= \frac{23}{20} [/tex]
[tex]5r= \frac{23}{20} -1[/tex]
[tex]5r=0.15[/tex]
[tex]r= \frac{0.15}{5} [/tex]
[tex]r=0.03[/tex]
Now, the only thing left is multiply our rate by 100% to express it as a percentage:
[tex]r=(0.03)(100)=3[/tex]%

We can conclude that the interest rate of Mikayla's savings account is 3%.

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