Question

A bank features a savings account that has an annual percentage rate of 3.6% with interest compoundedquarterly. Haley deposits $10,000 into the account.The account balance can be modeled by the exponential formula A(t) = a1, where is accountvalue after t years, a is the principal (starting amount), r is the annual percentage rate, k is the number oftimes each year that the interest is compounded.(A) What values should be used for a,r, and k?(21000000.036lo(B) How much money will Haley have in the account in 9 years?AnswersRound answer to the nearest penny.(C) What is the annual percentage yield (APY) for the savings account? (The APY is the actual or effectiveannual percentage rate which includes all compounding in the year).APYRound answer to 3 decimal places.Ok

Answer 1

Given data:

Principal (starting amount) = $10, 000

Interest rate compounded quarterly = 3.6% = 0.036

The modeled account balance is

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

SOLUTION A.

The values that should be used for a, r and k are:

`\begin{gathered} a=\text{ \$10,000} \\ r=3.6\text{ \% = 0.036} \\ k=\text{ 4 (compounded quartely)} \end{gathered}`

SOLUTION B

The money Hailey will have in the account in 9 years would mean that t = 9 years. Hence,

`\begin{gathered} A(t)=10,000(1+(0.036)/(4))^(4*9) \\ A(t)=10,000(1+0.009)^(36)_{} \\ A(t)=10,000(1.009)^(36) \\ A(t)=\text{ \$}13806.45 \end{gathered}`

SOLUTION C

The annual percentage yield (APY) can be calculated using the formula below

`\begin{gathered} \text{APY}=(1+(r)/(n))^n-1 \\ APY=(1+(0.036)/(4))^(^4)-1 \\ APY=(1+0.009)^4-1 \\ APY=(1.009)^4-1 \\ APY=1.0365^{}-1 \\ APY=0.03649 \\ APY=3.649\text{ \%} \end{gathered}`