Math Question
![A bank features a savings account that has an annual percentage rate of \( r=4.1 \% \) with interest compounded daily. Emanuel deposits \( \$ 7,500 \) into the account.
The account balance can be modeled by the exponential formula \( S(t)=P\left(1+\frac{r}{n}\right)^{n t} \), where \( S \) is the future value, \( P \) is the present value, \( r \) is the annual percentage rate, \( n \) is the number of times each year that the interest is compounded, and \( t \) is the time in years.
(A) What values should be used for \( P, r \), and \( n \) ?
\[
P=7500 \quad r \quad r=
\]
\[
\boldsymbol{n}=365
\]
(B) How much money will Emanuel have in the account in 10 years?
Answer \( =\$ 11300.87 \).
Round answer to the nearest penny.
(C) What is the annual percentage yield (APY) for the savings account? (The APY is the actual or effective) annual percentage rate which includes all compounding in the year).
\( A P Y=4.185 \quad \vee \% . \)
Round answer to 3 decimal places.](https://d3hlidq5bf9vg0.cloudfront.net/app-server-student/2021/11/15/b752c263-3b8f-44c2-8348-ae092020a696.png "A bank features a savings account that has an annual percentage rate of \( r=4.1 \% \) with interest compounded daily. Emanuel deposits \( \$ 7,500 \) into the account.
The account balance can be modeled by the exponential formula \( S(t)=P\left(1+\frac{r}{n}\right)^{n t} \), where \( S \) is the future value, \( P \) is the present value, \( r \) is the annual percentage rate, \( n \) is the number of times each year that the interest is compounded, and \( t \) is the time in years.
(A) What values should be used for \( P, r \), and \( n \) ?
\[
P=7500 \quad r \quad r=
\]
\[
\boldsymbol{n}=365
\]
(B) How much money will Emanuel have in the account in 10 years?
Answer \( =\$ 11300.87 \).
Round answer to the nearest penny.
(C) What is the annual percentage yield (APY) for the savings account? (The APY is the actual or effective) annual percentage rate which includes all compounding in the year).
\( A P Y=4.185 \quad \vee \% . \)
Round answer to 3 decimal places.")
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