Joseph deposited a certain amount of money.He earned one over nine of its principal at the number of years equal to the rate provided.Find the interest rate provided.**i need your help guys+++
(1+r/100)^r = 1/9
no real solutions. Let's try simple interest:
(r/100)*r = 1/9
r^2 = 100/9
r=10/3 = 3.33%
let's take $100
interest earned = 100/9
let the rate be r
then the number of years = r
100(r/100)(r) = 100/9
r^2 = 100/9
r = 10/3 = 3 1/3 % for 3 1/3 years
in general:
amount invested --- x
interest earned ---- x/9
rate ----- y/100
time ---- y
I = PRT
x(y/100)(y) = x/9
y^2 = 100/9
y = 10/3 , just like above
thanks for your solutions @steve and reiny
To find the interest rate provided, we need more information. The problem states that Joseph earned "one over nine" of the principal amount over a certain number of years.
Let's assume the principal amount is P and the interest rate is r (a decimal). The formula to calculate simple interest is:
I = P * r * t
where I is the interest earned, P is the principal, r is the interest rate, and t is the number of years.
According to the problem, Joseph earned "one over nine" of the principal amount after t years. Mathematically, we can express this as:
I = (1/9) * P
Substituting these values into the formula, we get:
(1/9) * P = P * r * t
Now, we can solve for the interest rate (r):
(1/9) = r * t
Divide both sides by t:
(1/9) / t = r
Simplifying further, we have:
r = 1 / (9t)
Therefore, the interest rate provided is 1 divided by nine times the number of years (t) specified in the problem.