Question

A bank features a savings account that has an annual percentage rate of r=2.8% with interest. compounded quarterly. Benicio deposits $8,000 into the account.

Answer 1

Step-by-step explanation

From the given question

We are given the formula to compute the amount that a sum of $8000 compounded quarterly will yield after time t at a rate of 2.8%

The formula is given by

`A(t)=a(1+(r)/(k))^(kt)`

Part A

`\begin{gathered} a=initial\text{ deposit= \$8000} \\ \\ k=number\text{ of times compounded in a year = 4} \\ \\ r=2.8\text{ \% =0.028} \\ \\ \end{gathered}`

part B

the amount in the account after 7 years will be

`\begin{gathered} A(t)=8000(1+(0.028)/(4))^(4*7) \\ \\ A(7)=\text{ \$}9725.57\text{ } \end{gathered}`

The amount that will be in the account after 7 years will be $9725.57

Part C

APY is given by

In our case we have

`\begin{gathered} APY=(1+(r)/(k))^k-1 \\ APY=\left(1+(0.028)/(4)\right)^4\:-1 \\ APY=1.02829-1 \\ APY=0.02829 \end{gathered}`

Hence, we will have the APY as

`\begin{gathered} APY=0.02829*100\text{ \% } \\ APY=2.829\text{ \%} \end{gathered}`

Hence, the APY is 2.829%