A sum of money is put on CI for 2 years at 20%. It would fetch Rs 482 more if the interest is payable half yearly than if it were payable yearly. Find the sum.Rs.10,000Rs.20,000Rs.30,000Rs.40,000

To solve this problem, we need to understand the difference between yearly and half-yearly compound interest.

1. Yearly compound interest: The formula for yearly 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, and t is the time the money is invested for in years. In this case, n=1 (since it's yearly) and t=2 (since it's for 2 years).

2. Half-yearly compound interest: The formula is the same, but n=2 (since it's compounded twice a year).

Given that the difference between the two is Rs 482 and the interest rate is 20% (or 0.20 in decimal), we can set up the following equation:

P(1 + 0.20/1)^(12) - P(1 + 0.20/2)^(22) = 482

Solving this equation will give us the principal amount P.

Let's simplify the equation:

P(1.2)^2 - P(1.1)^4 = 482 P(1.44) - P(1.4641) = 482 P(1.4641 - 1.44) = 482 P(0.0241) = 482 P = 482 / 0.0241 P = Rs 20,000

So, the sum of money put on compound interest is Rs 20,000.

To solve this problem, we need to understand the difference between yearly and half-yearly compound interest.

1. Yearly compound interest: The formula for yearly 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, and t is the time the money is invested for in years. In this case, n=1 (since it's yearly) and t=2 (since it's for 2 years).

2. Half-yearly compound interest: The formula is the same, but n=2 (since it's compounded twice a year).

Given that the difference between the two is Rs 482 and the interest rate is 20% (or 0.20 in decimal), we can set up the following equation:

P(1 + 0.20/1)^(12) - P(1 + 0.20/2)^(22) = 482

Solving this equation will give us the principal amount P, which is the sum of money that was put on compound interest.

Let's solve this equation:

P(1.2)^2 - P(1.1)^4 = 482 P(1.44) - P(1.4641) = 482 P(1.4641 - 1.44) = 482 P(0.0241) = 482 P = 482 / 0.0241 P = Rs 20,000

So, the sum of money that was put on compound interest is Rs 20,000.

To solve this problem, we need to understand the difference between yearly and half-yearly compound interest.

1. Yearly compound interest: The formula for yearly 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.

2. Half-yearly compound interest: The interest is compounded twice a year. So, n becomes 2 and the rate becomes half of the annual rate.

Given that the difference between the two scenarios is Rs 482, we can set up the following equation:

P(1 + r/n)^(nt) - P(1 + r)^(t) = 482

Substituting the given values into the equation:

P(1 + 0.20/2)^(2*2) - P(1 + 0.20)^2 = 482

Solving this equation will give us the value of P, which is the principal amount or the sum of money.

Let's solve this equation:

P(1.10)^4 - P(1.20)^2 = 482 P(1.4641) - P(1.44) = 482 P(0.0241) = 482 P = 482 / 0.0241 P = Rs 20,000

So, the sum of money is Rs 20,000.