question 3 (2 points)\nyou invest $2,000 in a 1 - year cd with 4% apr, compounded quarterly.\na) what is the…

question 3 (2 points)\nyou invest $2,000 in a 1 - year cd with 4% apr, compounded quarterly.\na) what is the apy? (round to 2 values after the decimal)\napy = ______ %\nb) how much total money will you have after 1 year? (round to the nearest cent)\nvalue in 1 year = $ ______\nblank 1:\nblank 2:

question 3 (2 points)\nyou invest $2,000 in a 1 - year cd with 4% apr, compounded quarterly.\na) what is the apy? (round to 2 values after the decimal)\napy = ______ %\nb) how much total money will you have after 1 year? (round to the nearest cent)\nvalue in 1 year = $ ______\nblank 1:\nblank 2:

Answer

Explanation:

Step1: Recall the APY formula

The formula for APY is $APY=(1 + \frac{r}{n})^{n}-1$, where $r$ is the annual percentage rate (APR) and $n$ is the number of compounding periods per year. Here, $r = 0.04$ and $n=4$ (compounded quarterly).

Step2: Calculate APY

$APY=(1+\frac{0.04}{4})^{4}-1=(1 + 0.01)^{4}-1=1.01^{4}-1=1.04060401 - 1=0.04060401\approx 4.06%$

Step3: Recall the compound - interest formula

The compound - interest formula is $A=P(1+\frac{r}{n})^{nt}$, where $P$ is the principal amount, $r$ is the annual interest rate, $n$ is the number of compounding periods per year, and $t$ is the number of years. Here, $P = 2000$, $r=0.04$, $n = 4$, and $t = 1$.

Step4: Calculate the value after 1 year

$A=2000\times(1+\frac{0.04}{4})^{4\times1}=2000\times1.01^{4}=2000\times1.04060401=2081.20802\approx$2081.21$

Answer:

Blank 1: 4.06 Blank 2: 2081.21