Given:
Compound interest for 2 years = 600 rupees
Compound interest for 3 years = 938 rupees

To find:
Rate of interest

Formula:
The formula to calculate compound interest is:
A = P(1 + r/n)^(nt) - P

Where:
A = the future value of the investment/loan, including interest
P = the principal investment/loan amount
r = annual interest rate (decimal)
n = number of times that interest is compounded per year
t = number of years

Solution:
Let's assume the principal amount is P and the rate of interest is r.

Step 1:
Using the given information, we can set up two equations using the compound interest formula.

For 2 years:
A = P(1 + r/n)^(nt) - P
600 = P(1 + r/n)^(2n) - P ----(1)

For 3 years:
A = P(1 + r/n)^(nt) - P
938 = P(1 + r/n)^(3n) - P ----(2)

Step 2:
To solve these equations, we need to eliminate the variables P and n.

Step 3:
Divide equation (2) by equation (1):

938/600 = [P(1 + r/n)^(3n) - P] / [P(1 + r/n)^(2n) - P]

Simplify the equation:

1.56333 = [(1 + r/n)^(3n) - 1] / [(1 + r/n)^(2n) - 1] ----(3)

Step 4:
Let's assume a value for n (number of times compounded per year). For simplicity, let's assume n = 1 (compounded annually).

Substituting n = 1 into equation (3):

1.56333 = [(1 + r/1)^(3*1) - 1] / [(1 + r/1)^(2*1) - 1]

1.56333 = (1 + r)^3 - 1 / (1 + r)^2 - 1

Step 5:
Simplify the equation:

1.56333 = (1 + r)^3 - 1 / (1 + r)^2 - 1

Multiply both sides by (1 + r)^2 - 1:

1.56333[(1 + r)^2 - 1] = (1 + r)^3 - 1

1.56333(1 + 2r + r^2 - 1) = (1 + r)(1 + 2r + r^2) - 1

1.56333(2r + r^2) = 1 + 3r + 3r^2 + r^3 - 1

1.56333r^2 + 3.12666r = 3r^2 + r^3 + 3r

0 = r^3 + (3 - 1.56333)r^2 + (3 - 3.12666)r

0 = r^3 + 1.43667r^2

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