answer of the effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half -yearly is
P = Po(1+r)^n.
r = (6%/2)/100% = 0.03 = Semi-annual % rate expressed as a decimal.
n = 2comp./yr. * 1yr. = 2 Compounding
periods.
P = Po(1+0.03)^2 = Po*1.03^2 = 1.0609Po.
I = P-Po = 1.0609Po-Po = 0.0609Po.
I/Po * 100% = 0.0609Po/Po = 6.09% = Effective APR.
To determine the effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly, follow these steps:
Step 1: Divide the nominal rate by the number of compounding periods in a year. In this case, since the nominal rate is payable half-yearly, the number of compounding periods in a year is 2. Therefore, divide 6% by 2.
6% / 2 = 3%
Step 2: Add 1 to the result from step 1 and raise it to the power of the number of compounding periods in a year. In this case, since there are 2 compounding periods in a year, raise the result from step 1 to the power of 2.
(1 + 0.03)^2 = (1.03)^2 = 1.0609
Step 3: Subtract 1 from the result from step 2 and multiply by 100 to get the effective annual rate as a percentage.
(1.0609 - 1) * 100 = 6.09%
Therefore, the effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is approximately 6.09%.