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%.......just did it on apex

Answer 2

Answer:

C. 1.9090%

Step-by-step 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.

$APY=(1+\frac{r}{n})^n-1$, 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.

$1.9\%=\frac{1.9}{100}=0.019$

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

$APY=(1+\frac{0.019}{2})^2-1$

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

$APY=(1.0095)^2-1$

$APY=1.01909025-1$

$APY=0.01909025$

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

$APY=0.01909025\times 100$

$APY=1.909025\%\approx 1.9090\%$

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