A certain sum of money becomes 8 times in 3 years interest being compounded yearly. Find out the number of years it would take to become 5 times at the same rate of interest but interest being counted on simple interest basis

To solve this problem, we first need to find the rate of interest.

Given that the sum of money becomes 8 times in 3 years with interest compounded yearly, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where: A = the amount of money accumulated after n years, including interest. P = the principal amount (the initial amount of money) r = annual interest rate (in decimal) n = number of times that interest is compounded per year t = time the money is invested for in years

In this case, A/P = 8, n = 1 (since the interest is compounded yearly), and t = 3. Substituting these values into the formula, we get:

8 = (1 + r)^3

Taking the cube root of both sides, we get:

2 = 1 + r

So, r = 2 - 1 = 1. This means the annual interest rate is 100%.

Now, we want to find out the number of years it would take for the sum to become 5 times on a simple interest basis. The formula for simple interest is:

A = P + Prt

Or, simplifying, A/P = 1 + rt

We know that A/P = 5 and r = 1, so we can substitute these values into the formula:

5 = 1 + 1*t

So, t = 5 - 1 = 4

Therefore, it would take 4 years for the sum to become 5 times at the same rate of interest on a simple interest basis.