Principle and Rate of Interest Calculation:

To find the principle and rate of interest, we can use the formula for calculating compound interest:

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

where:
A = the final amount of money
P = the principle (initial amount of money)
r = the rate of interest (in decimal form)
n = the number of times interest is compounded per year
t = the number of years

In this case, we have two sets of data:
1. After 2 years, the amount is $6,200
2. After 3 years, the amount is $7,400

Step 1: Finding the Principle (P)

Using the formula above, we can rearrange it to solve for P:

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

For 2 years:
P1 = $6,200 / (1 + r/n)^(2n)

For 3 years:
P2 = $7,400 / (1 + r/n)^(3n)

Step 2: Finding the Rate of Interest (r)

To find the rate of interest, we can use the following formula:

r = (n * ((A/P)^(1/(nt))) - 1)

For 2 years:
r1 = n * ((A1/P1)^(1/(n*2))) - 1

For 3 years:
r2 = n * ((A2/P2)^(1/(n*3))) - 1

Solving the Equations:

To solve these equations, we need to make some assumptions. Let's assume that the interest is compounded annually (n = 1).

For 2 years:
P1 = $6,200 / (1 + r)^(2)

For 3 years:
P2 = $7,400 / (1 + r)^(3)

By substituting the given values into the equations and solving for P, we can find the principle. Similarly, by substituting the given values into the equations and solving for r, we can find the rate of interest.

It is important to note that the actual values of P and r will depend on the interest compounding frequency (n) and the assumptions made in the calculation.

S.i of 1 year=7400-6200/3-2=1200

p = amount-2×s.i
p=6200-1200×2= 6200-2400=3800