Final answer:
Compound interest for Rs 40,000 at 16% per annum over 1.5 years with half-yearly compounding can be calculated using the formula A = P(1 + r/n)^(nt), leading to a significant increase in the future value of the investment.
Step-by-step explanation:
Calculating Compound Interest for a Half-Yearly Compounded Amount
To calculate the compound interest on Rs 40,000 at a rate of 16% per annum for 1.5 years with half-yearly compounding, you need to recognize that the interest rate will be compounded three times (since 1.5 years equals three six-month periods). Therefore, the effective interest rate for each compounding period will be half of the annual rate, which is 8%.
To find the future amount after 1.5 years, the formula A = P(1 + r/n)nt is employed, where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial sum of money), 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 or borrowed for, in years.
For this problem:
- P = Rs 40,000
- r = 16% per annum or 0.16 in decimal
- n = 2 (because interest is compounded half-yearly)
- t = 1.5 years
First, convert the annual interest rate to the rate per period by dividing by the number of periods per year. Then use the formula to calculate the future amount and subtract the principal to find the compound interest.
The calculation would therefore be:
A = 40000(1 + 0.08)^2*1.5 = 40000(1 + 0.08)^3
Once you compute the amount A, subtract the principal to get the compound interest earned over the 1.5 years.
Remember, compound interest can significantly increase the future value of an investment or loan compared to simple interest, particularly over longer periods and with more frequent compounding periods.