Question

If the APR of a savings account is 1.9% and interest is compounded semiannually, what is the approximate APY of the account

A. 1.9166%
B. 1.9136%
C. 1.9090%
D. 1.9151%

Answer 1

C. 1.9090%

Explanation:

We have been given that the APR of a savings account is 1.9% and interest is compounded semiannually. We are asked to find the APY of the account.

To solve our given problem, we will use APY formula.

`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 our given rate in decimal form.

`1.9\%=(1.9)/(100)=0.019`

Upon substituting
`r=0.019` and
`n=2` in APY formula we will get,

`APY=(1+(0.019)/(2))^2-1`

`APY=(1+0.0095)^2-1`

`APY=(1.0095)^2-1`

`APY=1.01909025-1`

`APY=0.01909025`

Since APY is in decimal form, so we will multiply APY by 100 to get as percentage.

`APY=0.01909025* 100`

`APY=1.909025\%\approx 1.9090\%`

Therefore, the the approximate APY of the account 1.9090% and option C is the correct choice.