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A bank features a savings account that has an annual percentage rate of 4.1 % with interestcompounded monthly. Zach deposits $3,000 into the account.How much money will Zach have in the account in 1 year?Answer = $Round answer to the nearest penny.What is the annual percentage yield (APY) for the savings account?%. Round to the nearest hundredth of a percent.APY=

A Bank Features A Savings Account That Has An Annual Percentage Rate Of 41 With Interestcompounded Monthly Zach Deposits 3000 Into The AccountHow Much Money Wil class=

Sagot :

It is given that the amount invested is $3000 with an interest rate of 4.1% compounded monthly.

It is required to find the amount in 1 year and the annual percentage yield.

The formula for Compound Interest is:

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

Where:

• A= final amount

,

• P= amount invested initially

,

• r= interest rate

,

• n= number of times interest is compounded in a year

,

• t= number of years

Substitute P=3000, r=4.1%=0.041, n=12 (compounded monthly), and t=1 into the formula:

[tex]A=3000(1+\frac{0.041}{12})^{12(1)}\approx\$3125.34[/tex]

The formula for the Annual Percentage Yield is given as:

[tex]APY=(1+\frac{r}{n})^n-1[/tex]

Substitute r=0.041, n=12 into the formula:

[tex]APY=(1+\frac{0.041}{12})^{12}-1\approx0.0418=4.18\%[/tex]

Answers:

Amount = $3125.34

APY = 4.18%

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