To solve this, we are going to use the simple interest formula: [tex]A=P(1+rt)[/tex]
where
[tex]A[/tex] is the total amount the company paid after [tex]t[/tex] years.
[tex]P[/tex] is the money that the company borrowed
[tex]r[/tex] is the interest rate in decimal form
Notice that if the company paid $2625 in interest, the total amount that the company paid was the interest plus the amount they borrowed, so:
[tex]A=25000+2625[/tex]
[tex]A=27625[/tex]
Next, we are going to convert the interest rate to decimal form. To do that we are going to divide the rate by 100%
[tex]r= \frac{3.5}{100} [/tex]
[tex]r=0.035[/tex]
Now we know that [tex]A=27625[/tex], [tex]P=25000[/tex], and [tex]r=0.035[/tex]. So lets replace those values in our simple interest formula to find [tex]t[/tex]:
[tex]A=P(1+rt)[/tex]
[tex]27625=25000(1+0.035t)[/tex]
[tex] \frac{27625}{25000} =1+0.035t[/tex]
[tex]1+0.035t=1.105[/tex]
[tex]0.035t=1.105-1[/tex]
[tex]0.035t=0.105[/tex]
[tex]t= \frac{0.105}{0.035} [/tex]
[tex]t=3[/tex]
We can conclude that the company repaid the money after 3 years.
