Helen borrowed $8,000 from her grandfather to pay for college. Five years later, she paid him back the $8,000 and an interest of $1,200 . What was the annual interest rate?

We have been given that Helen borrowed $8,000 from her grandfather to pay for college. Five years later, she paid him back the $8,000 and an interest of $1,200.

We will use following formula to find the annual interest rate.

[tex]I=PrT[/tex], where,

[tex]I= \text{Amount of interest}[/tex],

[tex]P= \text{Principal amount}[/tex],

[tex]r= \text{Annual interest rate in decimal form}[/tex],

[tex]T= \text{Time in years}[/tex].

Upon substituting our given values in above formula we will get,

[tex]1,200=8,000*r*5[/tex]

[tex]1,200=40,000*r[/tex]

Upon dividing both sides of our equation by 40,000 we will get,

[tex]\frac{1,200}{40,000}=\frac{40,000*r}{40,000}[/tex]

[tex]\frac{12}{400}=r[/tex]

[tex]\frac{3}{100}=r[/tex]

[tex]0.03=r[/tex]

Since our interest rate is in decimal form,let us convert it in percentage by multiplying 0.03 by 100.

[tex]r=0.03\times 100=3\%[/tex]

Therefore, the annual interest rate was 3%.