Find the total amount required to pay off a loan of 16000 plus interest at the end of 8 years if the interest is compounded half-yearly and the rate is 14% p.a.
16000(1+.14/2)^(2*8) =
To find the total amount required to pay off the loan, we need to calculate the compound interest on the loan and add it to the principal.
First, let's calculate the interest per compounding period. The interest rate is given as 14% per annum, which means it needs to be divided by the compounding periods per year (since the interest is compounded half-yearly).
Since the interest is compounded half-yearly, there are 2 compounding periods in a year. So, the interest rate per compounding period is 14% / 2 = 7%.
Next, let's calculate the total number of compounding periods for 8 years. Since the interest is compounded half-yearly, the total number of compounding periods is 8 * 2 = 16.
Now we can calculate the compound interest using the formula:
Compound Interest = Principal * (1 + (Interest Rate / 100))^Number of Compounding Periods
Substituting the values:
Compound Interest = 16000 * (1 + (7 / 100))^16
Now calculate the compound interest:
Compound Interest = 16000 * (1.07)^16
Using a calculator or spreadsheet, the compound interest is approximately 16000 * 1.9325 = 30920
Finally, we add the compound interest to the principal to find the total amount required to pay off the loan:
Total Amount Required = Principal + Compound Interest
Total Amount Required = 16000 + 30920 = 46920
Therefore, the total amount required to pay off the loan of $16,000 plus interest at the end of 8 years, compounded half-yearly at a rate of 14% p.a., is $46,920.