The difference between the compound interest and simple interest for a period of 2 years at the rate of 12% p.a. is Rs. 90. What is the principal?

To solve this problem, we need to use the formulas for compound interest and simple interest.

The formula for compound interest is A = P(1 + r/n)^(nt), where:

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

The formula for simple interest is I = Prt, where:

• I is the interest.
• P is the principal amount.
• r is the annual interest rate (in decimal).
• t is the time the money is invested for in years.

Given that the difference between the compound interest and simple interest for a period of 2 years at the rate of 12% p.a. is Rs. 90, we can set up the following equation:

Compound Interest - Simple Interest = 90

Substituting the formulas into the equation, we get:

P(1 + 0.12/1)^(12) - P - P0.12*2 = 90

Solving this equation will give us the principal amount P.