At what annual interest rate musts $2500 be invested for three years in order to yield $412.50 in simple interest? Do you not round the decimals to percent, change the decimals to percent and write it as a fraction.

Tutors, sign in to answer this question.

Simple interest means the interest money does not get added to the initial investment (principal) so you don't earn additional interest money on the interest you already earn.

Therefore to calculate the interest earned in one year, you multiply the initial investment or principal amount of money by the rate of interest per year. To get the interest for 3 years, just multiply by 3. In this example, you are already given the interest amount and asked to find the interest rate. in real life, it is usually the other way around. But in any case, the formula is the same.

Interest = Principal x Interest rate x Time

Because the interest rate is annual (per year), the time must also be expressed in years.

What we don't know is the interest rate so we will call it R.

So you get 412.50 = 2500. x R x 3 and you solve for R

R = .055 = 5.5% = 55/1000

The accumulated amount *A* is found using *A* = *P* + *
I*, where *P* is the Principal and *I* simple interest. Simple interest can also be written using
*I* = *P* × *r* × *t* =* Prt*, where *r* is the interest rate in number of dollars per year and
*t* the time in years.

The values of the given variables are: *P* = $2,500, *I* = $412.50 and
*t* = 3 years, so *A* = *P* + *I* = $2,912.50.

Since *A* = *P* + *I* and *I* = *Prt*, *
A* can be written as *A* = *P* + *Prt*. Solving this equation for
*r*:

Substituting the values to solve for the interest rate:

0.055 as a percent is 5.5/100 = 5.5%.

Checking, using the factored form of the amount equation:

Maggie:

Let r per cent be the annual rate of simple interest. For each $100 you get r dollars as interest after one year. For a principal of $2500 you get 25( r) each year. In three years you will get 3 x 25 r = 75 r as simple interest. You want this yield to be $412.50. So equate 75 r to $412.50.

75 r = 412.50 gives r = 412.50/ 75 = 5.5

Your answer is 5.5 % p.a.

Dattaprabhakar (Dr. G.)

Already have an account? Log in

By signing up, I agree to Wyzant’s terms of use and privacy policy.

Or

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Your Facebook email address is associated with a Wyzant tutor account. Please use a different email address to create a new student account.

Good news! It looks like you already have an account registered with the email address **you provided**.

It looks like this is your first time here. Welcome!

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Please try again, our system had a problem processing your request.

Paul K.

Experienced, Understandable and Memorable Math Tutor

$7.50 per 15 min

View Profile >

Linda L.

Experienced Science Teacher and Tutor, patient and innovative

$7.50 per 15 min

View Profile >

Susan J.

Latin, Vocabulary, History and Literature Tutor

$6.25 per 15 min

View Profile >