Final answer:
To find the principal amount that will grow to Rs 6000 in 2 years at a 10% annual interest rate, we use the compound interest formula, and the calculation shows that a principal amount of Rs 4958.68 needs to be invested.
Step-by-step explanation:
The student is asking about a compound interest problem where they need to determine the principal amount that will amount to Rs 6000 in 2 years at an annual interest rate of 10%. To solve this, we will use the formula for compound interest which 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, r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for.
Since the question specifies an annual compounding rate, n will be 1, and t is 2 years. We know that A, the final amount, is Rs 6000 and r is 10% or 0.1 in decimal form. Now, we need to find P.
Step-by-step solution:
- Convert the percentage rate to a decimal: r = 10% = 0.1.
- Substitute A, r, n, and t into the formula: 6000 = P(1 + 0.1/1)^(1*2).
- Simplify the equation: 6000 = P(1.1)^2.
- Calculate (1.1)^2: (1.1)^2 = 1.21.
- Divide both sides by 1.21 to solve for P: P = 6000 / 1.21.
- Perform the division: P = 4958.68.
The principal amount P that needs to be invested is Rs 4958.68.