. The nominal interest rate on your account is 7%; your semi-annually effective rate of interest (APY) will be
effective rate
=(1+i/n)^n - 1
where n is the number of compounding per year.
For 7% compounded semi-annually, n=2, and i=0.07
effective rate
=(1+0.07/2)²-1
= 7.1225%
To calculate the semi-annually effective rate of interest (APY), you can use the following formula:
APY = (1 + (nominal interest rate / number of compounding periods))^number of compounding periods - 1
In this case, the nominal interest rate is 7% and the compounding period is semi-annually (twice a year).
APY = (1 + (0.07 / 2))^2 - 1
Now, let's calculate the APY step-by-step:
1. Divide the nominal interest rate by the number of compounding periods:
0.07 / 2 = 0.035
2. Add 1 to the result:
1 + 0.035 = 1.035
3. Raise the result to the power of the number of compounding periods:
1.035^2 = 1.071225
4. Subtract 1 from the result:
1.071225 - 1 = 0.071225
Therefore, the semi-annually effective rate of interest (APY) is 0.071225, or 7.1225%.
To calculate the semi-annually effective rate of interest (APY) from the nominal interest rate, we need to use the formula:
APY = (1 + (r/n))^n - 1
Where:
APY = semi-annually effective rate of interest
r = nominal interest rate (expressed as a decimal)
n = number of compounding periods per year
In this case, the nominal interest rate is 7% or 0.07 as a decimal.
However, we need to know the compounding frequency (n) to calculate the semi-annually effective rate of interest. Could you please provide the compounding frequency?