Determine the rate of interest at which a sum of money will become 216/125 times the original amount in 1 and a half years, if the interest in compounded half

huh? Is it compounded twice a year? If so,

(1+r/2)^(2*1.5) = 216/125
(1+r/2)^3 = (6/5)^3
1+r/2 = 1.2
r/2 = .2
r = .4 or 40%

Bokachoda sala chutiya

To determine the rate of interest, we can use the formula for compound interest:

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

Where:
A: The final amount
P: The principal amount (original amount)
r: The annual interest rate (as a decimal)
n: The number of times interest is compounded per year
t: The time in years

In this case, we're given that the final amount (A) is 216/125 times the original amount (P) and the time (t) is 1.5 years. We need to find the interest rate (r).

Let's substitute the given values into the formula:
(216/125)P = P(1 + r/2)^(2 * 1.5)

Simplifying the equation further:
216/125 = (1 + r/2)^3

To isolate the term (1 + r/2), we can take the cube root of both sides:
∛(216/125) = 1 + r/2

Now, solve for r by subtracting 1 from both sides, and then multiplying by 2:
2 * (∛(216/125) - 1) = r

Calculate (∛(216/125) - 1), then multiply it by 2 to find the rate of interest.