A certain amount of money was invested in compound interest which amount to 2420 in 2 years and 2662 in 3 years.calculate the rate of interest and the sum of money invested ?

Let the principal amount be P and the rate of interest be r.

Using the compound interest formula:

A = P(1 + r)^n

Where:
A = Final amount
P = Principal amount
r = Rate of interest
n = Number of years

Given:
A1 = 2420
A2 = 2662
n1 = 2 years
n2 = 3 years

From the given data, we have:

2420 = P(1 + r)^2
2662 = P(1 + r)^3

Dividing the second equation by the first equation, we get:

2662/2420 = (1 + r)^3 / (1 + r)^2
1.1 = 1 + r
r = 0.1

Now, substitute the value of r back into the first equation to find the principal amount:

2420 = P(1 + 0.1)^2
2420 = P(1.1)^2
2420 = P(1.21)
P = 2420 / 1.21
P = 2000

Therefore, the principal amount invested is $2000 and the rate of interest is 10%.