Find the Compound Interest on a sum of Rs.1000 at the rate of 10% per annum for 1.5 years wheninterest is compounded half-yearly

Sure, here is the step by step solution:

Step 1: Identify the given values Principal (P) = Rs. 1000 Rate of interest (r) = 10% per annum Time (t) = 1.5 years Since the interest is compounded half-yearly, we need to adjust the rate and time accordingly.

Step 2: Adjust the rate and time for half-yearly compounding The rate becomes half, i.e., r = 10/2 = 5% per half-year The time becomes double, i.e., t = 1.5*2 = 3 half-years

Step 3: Substitute the values in the formula for compound interest The formula for compound interest is A = P(1 + r/n)^(nt), where A is the amount after time t, P is the principal amount, r is the rate of interest, n is the number of times interest is compounded per time period, and t is the time. Here, n = 2 (since interest is compounded half-yearly), so the formula becomes A = P(1 + r/2)^(2t)

Step 4: Calculate the amount (A) A = 1000(1 + 5/100)^6 = 1000(1.05)^6 = Rs. 1340.10

Step 5: Calculate the compound interest The compound interest is given by the formula CI = A - P CI = 1340.10 - 1000 = Rs. 340.10

So, the compound interest on a sum of Rs.1000 at the rate of 10% per annum for 1.5 years when interest is compounded half-yearly is Rs. 340.10.

Sure, here's how you can calculate the compound interest:

Step 1: Identify the principal, rate of interest, and time period. In this case, the principal (P) is Rs. 1000, the rate of interest (r) is 10% per annum, and the time period (t) is 1.5 years.

Step 2: Since the interest is compounded half-yearly, we need to adjust the rate of interest and the time period. The rate of interest will be halved and the time period will be doubled. So, r becomes 5% (10%/2) and t becomes 3 (1.5*2).

Step 3: Now, we can 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 (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

Step 4: Substitute the values into the formula: A = 1000 (1 + 0.05/2)^(2*3)

Step 5: Solve the equation to find the compound interest. A = 1000 (1 + 0.025)^6 A = 1000 * 1.1608 A = Rs. 1160.8

Step 6: Subtract the principal from the total amount to get the compound interest. Compound Interest = A - P Compound Interest = 1160.8 - 1000 Compound Interest = Rs. 160.8

So, the compound interest on a sum of Rs.1000 at the rate of 10% per annum for 1.5 years when interest is compounded half-yearly is Rs. 160.8.