Ask a question

Algebra word problem

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.

3 Answers by Expert Tutors

Tutors, sign in to answer this question.
Phillip R. | Top Notch Math and Science Tutoring from Brown Univ GradTop Notch Math and Science Tutoring from...
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
John K. | Effective Specialist in Never-Been-Good-at-Math situationsEffective Specialist in Never-Been-Good-...
4.7 4.7 (18 lesson ratings) (18)
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:
A - P = Prt and r = (A - P)/Pt.
Substituting the values to solve for the interest rate:
r = ($2,912.50 - $2,500)/($2,500)(3 years) = $0.055/year.
0.055 as a percent is 5.5/100 = 5.5%.
Checking, using the factored form of the amount equation:
A = P(1 + rt) = $2,500(1 + (0.055)(3)) = $2,912.50.
Dattaprabhakar G. | Expert Tutor for Stat and Math at all levelsExpert Tutor for Stat and Math at all le...
5.0 5.0 (2 lesson ratings) (2)
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.)