Jeremiah currently has an account balance of $1,624.35. His initial deposit on the account was $975 and it earned 3.7% simple interest. How long has Jeremiah held the account?

11 years

18 years

27 years

45 years

Question

Jeremiah currently has an account balance of $1,624.35. His initial deposit on the account was $975 and it earned 3.7% simple interest. How long has Jeremiah held the account? 

11 years 

18 years 

 27 years 

 45 years

mathstudent55 · Answer

Simple interest is given by the formula:
I = Prt
where I = interest, P = principal, r = rate, and t = time

SInce the account started with $975 and ended up with $1,624.35, how much of the final amount is interest?

anonymous · Answer

so do I divide by time?

mathstudent55 · Answer

One step at a time. First answer my question.

anonymous · Answer

649.35

mathstudent55 · Answer

The simple interest formula uses the principal amount, interest rate, and time to find the interest. You know the principal maount ($975), the interest rate (3.7%) and you want to find time, so you need to know how much interest was earned.
$1624.35 - $975 = $649.35
You are correct.

mathstudent55 · Answer

Now plug in all the info you have into
I = Prt and solve for t

mathstudent55 · Answer

649.35 = 975 * 0.037 * t

anonymous · Answer

I multiplied 975 by 0.037 and got 36.08 but since I don't have the time do I just plug in answers from the answer choices?

anonymous · Answer

Nevermind, I found the answer. B. 18 years
Thank you very much!

mathstudent55 · Answer

You have
649.35 = 36.075t
Now divide both sides by 36.075:
649.35/36.075 = 18
Answer: 18 years

mathstudent55 · Answer

correct

mathstudent55 · Answer

wlcm