The simple interest on a sum of money is 1/9 of the sum.The number of years is numerically equal to the rate percent per annum. The rate percent per annum is?
Thanks
To find the rate percent per annum, we need to utilize the formula for simple interest:
Simple Interest = (Principal x Rate x Time) / 100
Let's assign variables to the given information:
- Principal = P (the sum of money)
- Rate percent per annum = R (unknown)
- Number of years = N (which is numerically equal to R)
- Simple Interest = SI (which is 1/9 of the sum)
Now, we can rewrite the given information in the form of equations:
SI = (P x R x N) / 100 ... (Equation 1)
SI = (1/9)P ... (Equation 2)
Since both equations are equal to SI, we can equate them:
(1/9)P = (P x R x N) / 100
To simplify this equation, we can cancel out the P on both sides:
1/9 = (R x N) / 100
Now, we can substitute N with R (according to the given information):
1/9 = (R x R) / 100
1/9 = R^2 / 100
To solve for R, we can cross-multiply and take the square root of both sides:
R^2 = (1/9) x 100
R^2 = 100/9
Taking the square root of both sides:
R = √(100/9)
R = 10/3
Thus, the rate percent per annum is 10/3 or approximately 3.33%.
I = PRT
you told me I = 1/9P --> P = 9I
you told me r = t, where r is a stated percent
I = 9I(r/100)(r)
1 = (9/100)r^2
r^2 = 100/9
r = 10/3 = 3.3333..
the rate is 3 1/3%
check:
suppose we have $1000 for 10/3 years at 3 1/3 %
I = 1000(10/3)(10/300) = 111.11
and 1/9 of 1000 = 111.11
My answer is correct