SOLUTION: The simple interest earned on a principal of five hundred dollars at an annual interest rate of p percent is less than twenty-five dollars.Write an equation or inequality to model

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Question 1168549: The simple interest earned on a principal of five hundred dollars at an annual interest rate of p percent is less than twenty-five dollars.Write an equation or inequality to model the situation
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
simple interest formula is i = p * r * n
i is the interest
p is the principal
r is the rate of return per time period
n is the number of time periods.

when p = 500 dollars and i < 25 dollars, the formula becomes:
25 > 500 * r * n
it can also be written as:
500 * r * n < 25

using this formula, if you are given r, then you can solve for n, or:
if you are given n, then you can solve for r.

for example, if you are given n = 5 years, then the formula becomes:
500 * r * 5 < 25
simplify to get:
2500 * r < 25
divide both sides of this inequality by 2500 to get:
r < 25/2500 which simplifies to r < .01
when r = .01 and n = 5, the formula becomes:
i = 500 * .01 * 5
solve for i to get i = 25.
when r is less than .01, i will be less than 25.

for another example, if you are given that r = .005, then the formula becomes:
500 * .005 * n < 25
simplify to get:
2.5 * n < 25
divide both sides of this inequality by 2.5 to get:
n < 25/2.5 which becomes n < 10
when r = .005 and n = 10, the formula becomes:
i = 500 * .005 * 10
solve for i to get i = 25
when n is less than 10, i will be less than 25.

your solution is that the inequality is:
p * r * n < 25

p is the principal
r is the interest rate per time period.
n is the number of time periods.
25 is the interest.

the equation where this is derived from is:
p * r * n = i

p is the principal
r is the interest rate per time period.
n is the number of time periods.
i is the interest













Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

The simple interest earned on a principal of five hundred dollars at an annual interest rate of p percent is less than twenty-five dollars.Write an equation or inequality to model the situation
Simple Interest (SI) = Principal (P) * Time (T) * Rate (R), or in this case: PTR < 25, with T = 1 year

 

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