Question

Find the APY corresponding to the following nominal rate. 7​% compounded semiannually.

Answer 1

7.23%.

Explanation:

We are asked to find APY (Annual Percentage Yield) to the nominal rate of 7% compounded semiannually.

We will use annual percentage yield formula to solve our given problem.

`APY=(1+(r)/(n))^n-1`, where,

r = Annual interest rate in decimal form,

n = Number of times interest is compounded per year.

Let us convert 7% into decimal form.

`7\%=(7)/(100)=0.07`

Semiannually means two times per year.

`APY=(1+(0.07)/(2))^(2)-1`

`APY=(1+0.00583333)^(12)-1`

`APY=(1.00583333)^(12)-1`

`APY=1.0722900804298071-1`

`APY=0.0722900804298071`

`APY\approx 0.0723`

Let us convert 0.0723 into percentage by multiplying with 100.

`0.0723* 100=7.23\%`

Therefore, annual percentage yield would be 7.23%.