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.