a sum of money invested at a simple interest rate R increases to 5/3 times the original sum after 5 years. The value for R is?
1+5r = 5/3
5r = 2/3
r = 2/15 = 0.1333 = 13.3%
Well, this is quite an interesting question! If a sum of money increases to 5/3 times its original value after 5 years, then we can say that the interest rate, R, for this investment is quite "simple" indeed!
To calculate R, we can use the formula for simple interest:
I = P * R * T
Where I is the interest, P is the principal (the original sum of money), R is the interest rate, and T is the time in years.
In this case, we want to find R, so we can rearrange the formula:
R = I / (P * T)
Since the sum increases to 5/3 times the original value, the interest can be calculated as:
I = (5/3)P - P = (2/3)P
Plugging in the values for I, P, and T, we get:
R = ((2/3)P) / (P * 5)
Simplifying further, we find:
R = 2/15
So, the value for R, the interest rate, is 2/15. It seems like a rather "fractional" rate, but hey, nobody said investing was an exact science!
To find the value of R, we can use the formula for simple interest:
A = P(1 + RT)
Where:
A = final amount
P = original sum
R = interest rate
T = time in years
In this case, the final amount (A) is 5/3 times the original sum (P), and the time (T) is 5 years.
Thus, we have:
5/3P = P(1 + 5R)
Now, let's solve for R.
First, we can simplify the equation:
5/3P = P + 5PR
Next, we can cancel P from both sides:
5/3 = 1 + 5R
Now, let's isolate R:
5R = 5/3 - 1
Combine like terms:
5R = 2/3
Finally, divide both sides by 5:
R = (2/3) / 5
R = 2/15
Therefore, the value for R is 2/15.
To find the value of the simple interest rate, R, we can use the formula for simple interest:
I = P * R * T
where:
I = Interest earned
P = Principal (original sum of money)
R = Simple interest rate
T = Time period
In this case, we are given that the sum of money increases to 5/3 times the original sum after 5 years. This means the interest earned, I, is equal to 5/3 times the original sum of money:
I = (5/3)P
We are also given that the time period, T, is 5 years.
Plugging these values into the formula, we have:
(5/3)P = P * R * 5
Simplifying the equation, we divide both sides by P and 5:
5/3 = R
Therefore, the value of R (the simple interest rate) is 5/3.