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?
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%.
